Elwood P. Dowd (Stewart) is a middle-aged, amiable though somewhat eccentric man whose best friend is an invisible 6 foot 3.5 inch tall rabbit named Harvey. As described by Dowd, Harvey is a pooka, a benign but mischievous creature from Celtic mythology who is especially fond of social outcasts (like Elwood). Elwood has driven his sister and niece (who live with him and crave normality and a place in society) to distraction by introducing everyone he meets to his friend, Harvey. His family seems to be unsure whether Dowd’s obsession with Harvey is a product of his (admitted) propensity to drink or perhaps mental illness.
Elwood spends most of his time in the local bar, and throughout the film invites new acquaintances to join him for a drink (or to his house for dinner). The barman and regulars accept the existence of Harvey, and the barman asks how they both are and unflinchingly accepts an order from Elwood for two martinis.
Elwood’s sister, Veta Louise Simmons (Hull), tries to have him committed to a sanatorium. In exasperation, she admits to the attending psychiatrist Dr. Lyman Sanderson (Charles Drake) that, after so many years of putting up with the invisible rabbit, she sees Harvey every once in a while herself. This causes Dr. Sanderson to let Elwood out and lock Veta up. After sorting out the mistake, Dr. Chumley (Cecil Kellaway), head of the sanatorium, decides that to save the reputation of the sanatorium he must bring Elwood back. At one point, when her daughter asks how someone possibly could imagine a rabbit, Veta says to her “Myrtle Mae, you have a lot to learn and I hope you never learn it.”
When tracked down, Elwood goes through several ordeals, although he remains largely oblivious to the plans put in place for him by Dr. Chumley, Judge Gaffney (William Lynn), and Veta Louise. In a scene where Dr. Sanderson and his nurse Miss Kelly (Peggy Dow) follow Elwood into an alley at the back of his and Harvey’s favorite bar, Charlie’s, Elwood tells the incredible story of how he came to meet Harvey, and explains the way in which people react when they meet them.
Elwood also explains that Harvey has the power to stop time: “Did I tell you he could stop clocks? Well, you’ve heard the expression ‘His face would stop a clock’? Well, Harvey can look at your clock and stop it. And you can go anywhere you like, with anyone you like, and stay as long as you like. And when you get back, not one minute will have ticked by. You see, science has overcome time and space. Well, Harvey has overcome not only time and space, but any objections.”
In the final scene of the film, Elwood (along with everybody else) arrives back at the hospital. By this point, Dr. Chumley is not only convinced of Harvey’s existence, but has begun spending time with him on his own, with a mixture of admiration and fear.
Dr. Sanderson convinces Elwood to come into his office where he will receive a serum called Formula 977 that will stop Dowd from “seeing the rabbit”. As they are preparing for the injection, Elwood’s sister is told by their cab driver about all the other people he has driven to the sanatorium to receive the same medicine, warning her that Elwood will become “just a normal human being. And you know what stinkers they are.” Upset by the very thought of this, Veta halts the injection by banging on the examining room door, at which point Elwood comforts her and explains her tears to others with, “Veta’s all tired out, she’s done a lot today.”
As Elwood is leaving, Dr. Chumley asks Elwood for Harvey’s help, and Elwood, being the obliging fellow he is, makes no objection. Dr. Chumley, arm in arm with an invisible companion, asks “Have you ever been to Akron?”
After the gates to Chumley’s Residence are closed, and Elwood is leaving, he stops, turns around and has a conversation with an invisible Harvey, who is already back from his trip to Akron and reaffirms their friendship. Harvey opens the gate, and Elwood and his invisible companion saunter off towards the bus stop, following Veta and Myrtle Mae, towards the planned last stop of Charlie’s Bar and another drink.
Through the film, Elwood looks up at Harvey. Stewart, at 6’4″, decided that Harvey should be 6’8″ for the film, but the script lines stating that Harvey was 6′ 3.5″ were unchanged from the play.