Dennis Barlow, a young Englishman and aspiring poet, wins an airline ticket and travels to Los Angeles to visit his uncle, Sir Francis Hinsley, who has spent more than thirty years at a major Hollywood studio. Soon after his arrival, the elder man is fired by his employer, D.J. Jr., and, unable to cope, he takes his own life.
Sir Ambrose Abercrombie, a prominent English expatriate, convinces the young man to spend most of the money from his uncle’s estate on an extravagant burial at Whispering Glades cemetery and mortuary. There, Dennis becomes infatuated with Aimee Thanatogenos, a cosmetician who is idealistic and naïve, claiming to be named after Aimee Semple McPherson. The chief embalmer, Mr. Joyboy, is drawn to her as well, but she has no romantic feelings for him. Aimee idoes the owner of Whispering Glades, the seemingly sober figure of reverence, Wilbur Glenworthy, though in private he is a calculating businessman who treats the cemetery as a business venture.
Dennis soon goes to work at Happier Hunting Grounds, a pet cemetery run by the Reverend’s twin brother, Harry Glenworthy. He discovers that Aimee is captivated by poetry, though she doesn’t know who authored the lines; he courts her by reciting verses, while carefully avoiding telling her where he actually works. Aimee’s frustration with Dennis’s cynical attitude grows, and when she earns a promotion, he suggests they marry and live on her income. Following the Guru Brahmin’s dubious guidance, she accepts a dinner invitation from Joyboy, but her budding romance falters when she observes his codependent relationship with his morbidly obese mother.
Guided once more by the Guru, Aimee becomes engaged to Dennis. She invites him to her house, which had been condemned before completion due to the danger of landslides, but he leaves early, unsettled by tremors and her seeming disregard for safety. Dennis and Harry then meet Gunther Fry, a boy genius with an interest in rocketry, and allow him to set up shop at the pet cemetery. Joyboy brings his mother’s pet myna bird to be buried, but agrees to have the bird shot into orbit on one of Gunther’s rockets. Realizing Dennis is his rival for Aimee’s affections, Joyboy brings Aimee to the ceremony, and she is outraged when she sees Dennis performing the service.
Reverend Glenworthy, sensing limited profit in Whispering Glades once all the plots are sold, decides to transform it into a retirement community, but cannot act without a plan for handling the interred bodies. He learns of Harry’s scheme to launch bodies into space and proceeds to secure surplus rockets by hosting an orgy at Whispering Glades with top Air Force brass as the guests of honor. Dennis, in a bid to win Aimee back, tells her Whispering Glades will be shut down. She flees, fearing that what he has said might be true.
Aimee seeks solace with Joyboy, but he has been called away to touch up the first disinterred body—an ex-astronaut nicknamed “The Condor”—before it is launched. She locates the Guru at a bar, but he, in a drunken haze, urges her to jump out a window. Hurrying back to the cemetery, Aimee finds Reverend Glenworthy, who confirms Dennis’s claim and tries to seduce her with the promise of continued employment at higher pay at the new facility. With her faith in everything she once held sacred fractured, Aimee calmly hooks herself up to an embalming machine.
Joyboy discovers Aimee’s body. Fearing a scandal, he calls Dennis to arrange her disposal in the pet cemetery’s crematorium. In exchange for a first-class ticket back to England and all the money in Joyboy’s bank account, Dennis agrees. As he is about to leave Whispering Glades, he changes his mind and plans to place Aimee’s body in the rocket’s casket to cremate The Condor. After watching the launch on television, Dennis boards his own plane, ending the sequence of events with a quiet, unresolved turn toward a new horizon.