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In England, Professor Alex Bolt is awarded the Nobel Prize for developing a universal language called Unispeak. Ray Whiteley, a United States ambassador who aspires to be president, has convinced the U.S. to fund a worldwide Unispeak project, believing that the non-controversial subject matter can only enhance his reputation. As head of the project, he commissions Alex's Italian wife Rhonda, an internationally acclaimed artist, to sculpt a statue commemorating Alex's achievement that will be erected in London's Grosvener Square. When asked by newsmen what Unispeak means to her, Rhonda jokes that since her husband became involved with the language, they rarely see each other. After a prolonged business trip, Alex returns home, where Rhonda proudly shows him the statue in her studio, which is an eighteen-foot nude in his likeness. Realizing that he is embarrassed by the thought of his nude image being displayed in a public park, she is angered by his prudishness and reminds him that the human figure has always been the subject of art. When she refuses to alter her work, Alex confers with his lawyers, Sir Geoffrey and Humphrey, about finding a legal way to prevent the statue's display, but they say he must prove that it is defamatory and suggest he should not have posed for it. Later, Alex complains to his friend Harry, an advertising man trained as a psychiatrist, that he never posed for it. Harry suggests that Alex discuss the problem with Ray, with whom he is appearing that evening on a television show featuring Unispeak. During the broadcast, Alex denounces the cost of the statue, which annoys Ray, who has not seen the work, and further angers Rhonda. After the show, Alex's colleague and assistant, Pat Demarest, points out that the statue's head resembles him, but the genitalia does not. Alex returns home demanding to know the identity of "Charlie," the nickname he gives the statue's offending anatomy. Equally angry, Rhonda says she has expressed in her art her dissatisfaction at seeing him only eighteen days in the last three years. Presuming that Rhonda had an affair with the model, Alex becomes jealous. After Geoffrey recalls how an actress proved defamation and won a lawsuit by naming the model whose breasts were advertised as her own, Alex vows to find the man. He takes secret photos of the statue's penis and then goes to a photo booth to take pictures of his own, both of which he shows to Harry, who confirms they are "two different fellows." Alex then bribes his housekeeper for a list of men who visited his house while Rhonda worked on the statue. He questions a household employee, the Paraguayan Joachim, who mistakes Alex's questions for a homosexual overture, tries to beat him up and then complains to his consulate. Next, noting that several of the men on the list frequent a Turkish bathhouse, Alex visits them in the sauna one at a time, until the attendant becomes suspicious that he is behaving inappropriately and throws him out. Humiliated, Alex talks to Harry, who suggests that he reconcile with Rhonda. Taking his advice, Alex showers Rhonda with gifts, flowers and wine, and she forgives him. Although Rhonda offers to tell him the name of the model she used for the statue, Alex generously claims it no longer matters. However, the specter of the sculpture haunts Alex in bed and, finding himself impotent, he blames Charlie, prompting Rhonda to banish him from their home. Ray, an adulterous womanizer, learns about Alex's bathhouse scandal from one of his paramours, and later about Joachim's complaint, and fears that the bad publicity will affect his own career. After flattering Rhonda into letting him see the statue before it is unveiled, Ray is shocked by its nudity and doubts the integrity of Alex, who he assumes posed for and approves of the statue. He later complains to his advisors that it is "a mile high and naked as a peeled banana." Although the president orders him to prevent the statue from being displayed, Ray's advisors report that he is legally bound by his contract with Rhonda. Worried about Alex's involvement in other scandals, the chief of the C.I.A., an elderly woman, suggests putting a "tail" on him. She sends her man, Hunter, to investigate Alex, who, with Pat's help, continues to check out the men on the list. One of the men, singer Hank Wills, is performing in a rock musical, Skin , during which the cast disrobes for the last song and performs in the nude. Alex attends a performance and sneaks onto the stage, where he blends in with the actors by removing his clothes and photographs the bare Hank. Hunter also strips, and takes photos of Alex. Still troubled by the statue's nudity, Ray sneaks into Rhonda's studio and attaches a fig leaf to it. Although angry about the vandalism, Rhonda lets Ray take her to a Japanese restaurant, where he simultaneously tries to seduce her and explain his position. He says he is trying to avoid criticism from the "do-gooders," who will scream at him for financing nudity and decadence, and the "pinko intellectuals," who will complain about censorship and repression. Alex and Pat take a private plane to a yacht where friends, three of whom are on the list, are vacationing with their wives. Over lunch, Alex carefully manipulates the conversation toward convincing them to play a "sociological game" in which they take bets and guess the order their respective spouses put on items of clothing. Surreptitiously, Hunter captures on film how the women recreate their morning dressing routine for Pat and the men do the same for Alex, who is then able secretly to compare their privates with the statue's. Later, when Ray sees Hunter's photos, he concludes that Alex is a wife-swapping, exhibitionist, homosexual voyeur. He confronts Alex and offers to protect him from scandal, if he will sign a statement saying that he was "out of his mind" to pose for the statue. When Alex explains that he never posed and that he needs to find the model to obtain a legal injunction, Ray arranges for the president to provide the entire resources of the U.S. government to check the other names on Alex's list. Under various pretexts, they arrest and search several of the men. Of the two remaining men on the list, one is Jacques Tremont, a sex-crazed artist who is on retreat in a reclusive, mountain-top Greek monastery. The only way to enter is to ride a cart that is attached to a pulley and hand-cranked up the steep mountain. When a first attempt to talk to Tremont fails, Alex and Ray's assistant, Chuck, hire prostitutes, who are flown by helicopter to the monastery, where they entice Tremont to join them and then fly him to their bordello. Later, the prostitutes tell Alex that Tremont's anatomy does not match their picture. Alex declares that he is disgusted by their search and tells Harry he wants to quit. However, as there are only two days before the unveiling and only one name left to check, Harry urges him to accomplish his original goal, so that he does not later suffer from "unresolved hostility" and "residual aggression." Soon after, men hired by Ray break into Rhonda's studio to saw off Charlie from the rest of the statue and steal it. Believing that Alex is responsible, Rhonda calls the police to investigate and refuses to believe his protests that he is innocent. Following Harry's advice, Alex proceeds to Florence, Italy, where the last man on the list, Rhonda's elderly teacher Guido Martinello, resides. At first unaware that the Italian police are pursuing him, Alex manages to visit with Guido, to whom he shows the photograph of the statue. However, before Guido can tell him the name of the model, police break into Guido's house and Alex flees. While evading the police, Alex passes the statue of David by Michelangelo and recognizes it as the object of his quest. Later, Ray reports to the president that Rhonda has agreed to create a new sculpture. To his embarrassment, when the new statue is unveiled, it proves to be a nude resembling Ray.