The family discovers Marge's secret fear, after they try to go on vacation with Homer's free airline tickets. On Lisa's advice, Marge visits a psychiatrist to get down to the bottom of her seemingly unexplainable fear.
Lenny, Carl and Barney pull life-threatening pranks on Moe, who laughs off each one. When Homer pulls a harmless and quite lame prank on Moe, he gets booed for it and is banned from the bar, with Moe taking a caricature of Homer off the wall and pulling Homer's favorite song ("It's Raining Men") out of the jukebox. Homer visits all the other bars in Springfield (including Cheers), but finds none of them to his liking.
The last bar in Springfield he comes to is "The Little Black Box", a private bar only for airline pilots. Homer pretends to be one, but is shortly rushed onto a plane when a temporary pilot is needed. Not knowing how to operate it, Homer accidentally damages the plane. In exchange for his silence regarding the incident, the carrier (Cwazy Clown Airlines) offers Homer and his family a trip to anywhere in the United States (except for Hawaii and Alaska, "the freak states").
Homer eagerly tells his family about their free trip, and everyone seems overjoyed, with the exception of Marge. On the plane, Marge freaks out, revealing to Homer that she has a fear of flying, and demands to be let off. After the traumatic incident, Marge begins to show bizarre behavior, which Lisa sees as suppressing her fear. Homer suggests ignoring Marge's behavior, but this soon reaches the point where he takes her advice and Marge goes to a psychiatrist (played by Anne Bancroft) to deal with her problems. Bart sits right next to the window, but then he hears Maggie crying because she is suffering from gas. Homer accepts but is opposed to this, because he thinks the shrink will tell her to break up with him, which is confirmed to the audience when the psychiatrist writes down 'husband' in large letters on her pad and underlines it.
Through the psychiatrist, Marge begins to explore more about her past. The psychiatrist has Marge remember one of her earliest traumatic experiences, causing Marge to remember her first day of school. After Patty and Selma upset her about scary things to expect, Marge was later ridiculed on the bus for liking The Monkees.
Sometime afterward, Marge relates about a dream in which she played the Mother from the TV show "Lost in Space," with Homer playing Dr Smith, and Lisa as Robby the Robot. At the end of the dream, as a spacecraft lifts off, Marge remarks how she yelled for her Father not to go.
When the psychiatrist tries to press Marge for more information, Marge is hesitant and tries to change the conversation. After some time, Marge relents, and explains how she saw her father board a plane, while her Mother explained that he was a pilot. Marge eagerly goes into the plane, only to see that her father was a steward (or to her, a "stewardess") and not a pilot as she was told.
This upsets her, until the psychiatrist explains that Mr. Bouvier helped make male flight attendants common. Even though the psychiatrist feels this is the root of her mental issues, Marge also remembers other things (a relative trying to feed her as a baby and failing, playing as a child with a small airplane that catches fire, Marge and her mother being attacked by a plane in a cornfield). She is about to tell Marge about the problem of her husband but Homer pulls her out of the session before she can.
Cured of her anxiety, she finally gets on a plane filled with confidence; this turns to annoyance as the plane overshoots the runway and lands in the sea.
In its original American broadcast, "Fear of Flying" finished 48th (tied with Dateline NBC) in the ratings for the week of December 12 to December 18, 1994, with a Nielsen rating of 9.6. The episode was the third highest rated show on the Fox network that week, beaten only by Beverly Hills, 90210, and Married... With Children.
Since airing, the episode has received many positive reviews from fans and television critics. Warren Martyn and Adrian Wood, the authors of the book I Can't Believe It's a Bigger and Better Updated Unofficial Simpsons Guide, said it was "a good Marge-centric episode with plenty of clever set pieces - the tributes to Cheers and Lost in Space are fantastic", and noted that "Marge's father looks suspiciously like Moe".