An inventor's unbreakable glass attracts the attention of businessmen and gangsters.

While crossing a busy intersection in Los Angeles, Augustus "Red" Pirdy, an accident-prone inventor who has devoted his life to safety, is struck by a taxicab. Although Red is not seriously injured in the accident, the Yellow Cab Co., fearing a lawsuit, sends its claims adjuster, Ellen Goodrich, to discuss a settlement with Red. Red admits that the accident was his fault and is about to sign a document that will absolve the company of any responsibility when Martin Creavy, an unscrupulous attorney, tries to persuade him to reconsider. Creavy suggests that Red instead sue the cab company for a large sum of money, but Red rejects his advice. When Red reveals that he has invented a special type of unbreakable glass, which he calls "Elastiglass," Ellen and Creavy see the potential in Red's discovery and begin vying for his confidence. Red eventually decides to put his trust in Ellen when she suggests that he try to sell his glass to the Yellow Cab Co. for the manufacture of safety windshields. Creavy, however, does not give up, and the following day he uses blackmail to force Willis Tomlin, a Yellow Cab Co. executive, to help him sabotage Red's efforts to sell his patent to the cab company. As part of his plan, Creavy arranges to have Tomlin replace the Elastiglass with regular glass just before Red demonstrates his invention for the cab company. Because of the switch, the demonstration ends in disaster and Ellen is demoted to the company's lost and found department. Later, Mickey Corkins hires Red to be a cab driver with the company, hoping that will get a second chance to demonstrate his invention. Though Red bungles his first attempts at driving a cab, Mickey persists in training him, and he eventually becomes a licensed Yellow Cab driver. Creavy, meanwhile, devises a plan to force Red to reveal his Elastiglass formula and sends one of his accomplices to frame Red in a taxicab accident. After the "accident," Creavy volunteers to act as Red's attorney, and has Dr. Byron Dokstedder, another one of his accomplices, pose as a psychiatrist sent to examine Red. Dokstedder tries to use hypnosis to force Red to reveal the secret of his unbreakable glass, but the session is interrupted when a sprinkler system in Red's living room is accidentally activated and the apartment is flooded. Meanwhile, at the cab company, Willis tells Ellen about the switched glass and vows to arrange another demonstration for Red. Ellen, who has fallen in love with Red, later tells him the good news at a home furnishings trade show, but Red is distracted by Dokstedder's hypnotic suggestions to avoid Ellen. After leaving the show, Red is knocked unconscious by Creavy's accomplice, Hugo, and is given an injection of truth serum to make him talk. Red, however, manages to escape by creating a diversion, and races to the Yellow Cab Co, where he discovers Willis murdered. Because Dokstedder had planted the idea in his mind that he was planning to kill Willis, Red becomes deeply confused and begins to believe himself to be the murderer. While Ellen and Mickey search for Red, Creavy and Dokstedder find Red and inject him with more truth serum. Red reveals the secret formula, but when he continues his drug-induced chatter and explains that he has proof that Creavy was responsible for Willis' death, Creavy decides to kill Red and dispose of his body at the home funishings trade show. By coincidence, Mickey and Ellen are at the trade show auditorium searching for Red just as Creavy and his men are about to kill him. Ellen is captured by one of Creavy's men, but she and Red manage to escape by driving a car onto the main floor of the trade show. As a wild chase ensues throughout the auditorium, Mickey summons a brigade of cab drivers, who arrive in time to save Ellen and Red. Creavy and his men are eventually apprehended, and Red finally gets a second chance to demonstrate his Elastiglass.