Professor Philip Brainard (Robin Williams), of Medfield College, is a mad scientist who is developing a new energy source in an attempt to raise enough money to save the college from closure. His preoccupation with his research distracts him from his fiancée, Sara Jean Reynolds (Marcia Gay Harden), who is the president of the college; he has already missed two wedding dates as a result of this, much to Sara’s anger. On the day of the third attempted wedding, Brainard is approached by his former partner Wilson Croft (Christopher McDonald), who has profited from ideas he has stolen from the chemist and now desires to steal Sara from Brainard and make her his wife, an intention that he declares directly to Brainard, who takes it as a joke. Before he can make it to the wedding, his latest experiment shows quick progress, forcing him to miss this latest wedding date. The resulting substance created from the experiment is a sentient green goo with enormous amounts of elasticity and kinetic energy. It increases in speed as it bounces and proves to be difficult to control, wreaking havoc on the neighborhood before the professor finally manages to capture it. Weebo (voiced by Jodi Benson), Brainard’s hovering robot assistant, classifies the substance as “flying rubber”, leading Brainard to christen it “Flubber”.
Brainard continues to work on Flubber into the early morning, looking to stabilize the Flubber’s movement as opposed to stimulation. Brainard’s incorrectly set watch alarm goes off at 6:30 a.m. and Weebo informs him that he has missed the wedding. Brainard goes to Sara’s office and unsuccessfully attempts to explain the situation to her. Meanwhile, Medfield College sponsor Chester Hoenicker (Raymond J. Barry) is disappointed that Brainard has failed his son Bennett (Wil Wheaton) in chemistry class. That night, Hoenicker sends his security guards Smith (Clancy Brown) and Wesson (Ted Levine) to Brainard’s house in an attempt to persuade Brainard into giving Bennett a better grade. However, Brainard is too busy testing the Flubber to even notice them and unknowingly knocks them unconscious with a Flubber-coated golf ball and bowling ball. He uses Flubber to give his vintage Ford Thunderbird flight. During a test run, he discovers Wilson flirting with Sara (making a bet that she’ll buy him dinner if Medfield wins, or join him for a weekend in the mountains if they lose). Afterward, Weebo attempts to confess her love of Brainard, only to be shrugged off as a computer. In response, she secretly creates a holographic human version of herself named Sylvia (Leslie Stefanson) in hopes of winning him over. Before Weebo can kiss Brainard in this form as he sleeps, Brainard awakens with another idea for Flubber. He enters a vacant basketball arena and tests the effects of Flubber on a basketball and his shoes. Later, he gives Flubber-padded shoes to the unskilled Medfield basketball team to increase their abilities and defeat their opposing team, Rutland.
Back in Brainard’s home, looking to have some fun, Weebo unleashes Flubber from his case, allowing him to dance around the house and cause general mayhem. After the close but successful basketball game, Brainard’s attempt to win Sara back into his favor fails. Upon returning home, Brainard releases his emotional baggage on Weebo, saying his absent-mindedness is due to his love of Sara. Weebo records Brainard’s ramblings and shows the footage to Sara, who then reconciles with Brainard. Brainard demonstrates Flubber’s abilities to Sara and they discuss how it can be used for profit. However, Hoenicker discovers Flubber’s existence and, after failing to convince Brainard and Sara to sell it to him, summons Smith and Wesson to raid Brainard’s house and steal Flubber. Weebo attempts to fend off the henchmen, only to be struck down by Wesson with a baseball bat. Brainard and Sara return to find the home a wreck and find Weber (Brainard’s house-robot) cleaning up, Flubber stolen, and Weebo destroyed. Later, Brainard discovers that Weebo had downloaded backup data of herself onto his computer in the event of her destruction, as well as a video recording of Weebo’s hologram professing her love for him.
Brainard and Sara confront Hoenicker and attempt to save Flubber, under the guise of accepting Hoenicker’s offer. While there, they discover that Wilson is allied with the millionaire who wanted to sell it for a profit. Brainard and Sara then reveal their ruse and unleash Flubber, starting a battle between them and the villains. In the end, Brainard and Sara defeat Wilson, Bennett, Hoenicker and his henchmen, retrieve Flubber, raise enough money to save the college, and finally have a successful wedding, along with Flubber and the “daughter” of Weebo, called Weebette. The film ends with the family heading to Hawaii in the Thunderbird, flying at an altitude of 30,000 feet.