As Ben Grimm and Johnny Storm look on, Reed Richards tests the nature and extent of Sue Storm;s invisibility power with a nuclear measuring device. When the test is finished Johnny decides to pull a prank and heat up the floor where Ben is standing. Annoyed, Ben grabs a chemical foam fire extinguisher/ But instead of hitting Johnny, the foam heads for Sue who suddenly summons up a shield of invisible energy that keeps the noxious chemical from touching her. Reed, Johnny, and Ben are astonished at Sue's new ability, and Reed assets that the radiation from his measuring device must have increased Sue's power. But the shield is still too thin, Reed says. He urges her to concentrate on making a stronger, thicker shield, which she does. Reed then tells the Thing to slam into the shield as a test. Ben manages to bend the shield, but he finds that he cannot break it. Then Johnny tries to burn through it, but even the most intense flame he can produce (without destroying the lab) fails to penetrate it.
The testing is interrupted when a police officer appears at the door. Reed's electronic sentinel device photographed the officer's badge and checked his identity in just two seconds before unlocking the door and admitting him. The officer explains that the police have been receiving complaints about the Fantastic Four's ICBM but Reed tells the policeman that he has a special CAA (Civil Aeronautics Administration) permit that allows him to keep it in the Baxter Buildings. As Reed escorts the policeman out, the Thing answers the telephone. The switchboard is suddenly deluged with complaint calls, the Thing angrily grinds the phone to powered. No sooner does the Thing stalk from the room in disgust that two more people appear at the door, looking for the Human Torch. Pierrer Picolino, the famous sculptor, has brought his lawyer to sue the Torch for damages to a priceless piece of abstract sculpture titled “Twilight Over Hoboken.” When the Torch flew by the artist's window, the heat of his flame turned the sculpture into slag. Abruptly, the sculptor an dhis lawyer find themselves in the air and speeding out of the room, down the hall, and into the elevator. Sue demonstrating another new invisibility power, turned a wheeled tea tray invisible and used it to ferry the two characters away. Upon analysis, Sue's team mates discover that she cannot remain invisible while making something else invisible. But it she chooses to remain only partly visible, then she can make the corresponding part of something else invisible.
Another telephone call ( a wrong number) interrupts their discussion. Then several remembers of the Women's Canasta and Mah Jong Society appear at the door with more complaints, but the Thing, turned invisible by Sue, holds up some spare robot parts, so that he look like a bizarre creature, and scares the women away. Reed regrets having forgotten to turn on the alarm system and lock the doors after the policemen left. Then he finds a pamphlet in the mail advertising a small, deserted island for sale off the coast of New Jersey. It would be an idea place, he says, to store their ICBM and other pieces of dangerous equipment that people have complied about. Soon the Fantastic Four are heading for the island in their U-car. But when they arrive, they find that the island is surrounded by an impenetrable barrier reef. The Human Torch melts a section of the reef into a causeway for his team mates to cross. As they examine the eerie piece of real estate, the Thing suddenly notices that something is dragging the U-car underwater. The Torch dives after the vehicle but when the water around him turns to steam, he is nearly suffocated. Ben and Reed pull Johnny to safety.
Annoyed at the loss of U-car and at being stranded on the rocky isle, the Fantastic Four spot a figure hiding in the shadow. They chase the figure into a cavern, but just as Reed extends his arms to capture him, a rock formation shaped like a pair of giant handcuffs falls on Reed's wrists. The Thing shatters the rock with one blow. Then the Fantastic Four confront their old foe, the Mole Man, who is leading an army of small, pale, yellow humanoid creatures. The Mole Man welcomes the Fantastic Four to his underground kingdom, which he calls Subterranea. He explains that he went to considerable trouble to get them there. He arranged to have the complainers bother them, and he made sure that the remote island ad arrived at just the right time. Then he pulls a lever than opens a chasm beneat the foursome, and they plummet into a large, circular net. A column of rising warm air acts as a broke to keep them from falling too fast. When the Thing tried to get off the net, Reed pulls him back, warning him that the surrounding wall is radioactive. The Mole Man seated in a plush chair amid his subterranea subjects, says that after their previous encounter he escaped from the Monster Isle through a vast system underground tunnels excavated by his loyal subterraneans. While he waited for this moment of revenge, he and his subjects construed enormous hydraulic platforms under all of Earth's largest cities. At a signal from him, the platforms will lower the cities into the Earth's core. When the governments of Earth find their largest cities missing, he continues, they will fire their missiles at each other, inflicting unimaginable destruction. The Mole Man will then emerge to rule what surface-men still survive. It will be the Fantastic Four's privilege to witness the Earth's destruction, totally unable to lift a finger in assistance.
The Mole Man orders one of his subjects to bring him the control mechanism that will cause New York and Moscow to vanish into the bowels of the Earth. But Sue projects her invisible shield around the device, and the Mole Man cannot touch it. Frustrated, he pounds the shield with his fists and his safety over the radioactive wall and capture the Mole Man. But after they jump over, the Mole Man's subterraneans prevent them from reaching him. The Mole Man pulls a series of sashes that open trapdoors in the floor, each an entrance into a specially designed trap. The first trapdoor pulls the Human Torch into a deep pit with powerful vacuum blast and before Reed can catch him, the trapdoor slams shut and two more open beneath Reed and Sue. The Thing runs to their aid only to be captured by a fourth trapdoor.
The Thing finds himself in a large chamber filled with a soft cottony substance. Although he is at first almost comfortable, he finds his strength useless when he tries to escape. Finally he locates the pipes that are piping the material in the chamber and yanks them from the wall. Then he enters the main outlet tunnel and heads for his rendezvous with the Mole Man. Sue finds herself in a pleasant room, but the Mole Man appears on a view screen and announces that she has 30 seconds to find her way out before a cylinder of nerve gas explodes and fills the chamber. She soon discovers that much in the room is an illusion and that 30 seconds is far too little time to find an actual exit. Thinking fast she decides that her power make things invisible might also work in reverse, to make invisible thing visible, so she scans the room with a beam of the invisible door. Because she is making the door visible, she herself turns invisible.
Reed discovers that the walls of his prison are made of non-porous plastic, and it is impossible for him to find a crack to squeeze through. As the Mole Man's nerve gas seeps into the chamber, Reed rolls himself into a hard, tight ball and holds his breath. Then by tensing his muscles and expanding he exerts enough pressure to break the chamber's wall. Exhausted from his efforts he falls to the floor in a heap. When he recovers, he finds himself by chance in the Mole Man's control room and he quickly begins rearranging the circuitry. The walls of the Human Torch's chamber have photoelectric cells that activate a mechanism that automatically extinguishes his flame whenever he tries to ignite. Sheets of ice emitted from the wall cover him, but he uses an ice shard to shatter the mechanism then burns out of the trap.
The thing slowly wades through the subterraneans who try to prevent him from attacking the Mole Man. He realizes that their limited mentalities make them innocent of any wrongdoing' they cannot help their slavish obedience to the Mole Man's will. So Ben carefully avoids harming any of them as eh pushes them out of the way. When the Mole Man sees the Thing break free of the subterraneans, he plunges the chamber into darkness. Possessing a radar like sense that allows him to function in total darkness, the Mole Man strikes the Thing with his staff and pitches him into a deep chasm. But just then, Reed appears and he snakes his arms around Ben, who grasp it as he falls. Reed then shapes his arm into a spiral ramp, and the Thing climbs out of the hole. The Mole Man pulls a switch that releases a ten-ton rock onto Reed and Ben. Reed hears the whistle of the falling object, but suddenly the Human Torch appears and vaporizes the rock with low – intensity nova blast. With the Torch's flame illuminating the chamber, the Mole Man realizes that he must retreat, and he escapes through a tunnel. She appears to tell them that she has found their U-car aside with a large stalactite. Reed explains that eh has not suddenly become a coward. He know that Mole Man is heading for his control mechanism and intends to plunge the Earth into World War 3. But the Mole Man does not know that Reed had disconnected the control button from all the hydraulic platform and has arranged for only this island to sink. The Mole Man's equipment will be render forever inoperable. No sooner does the U-car leaves than the island sinks into the sea, presumably taking the Mole Man with it.