Set in 1951 in South Korea, the 4077th Mobile Army Surgical Hospital is assigned two replacements: Captains "Hawkeye" Pierce and "Duke" Forrest, who arrive in a stolen Jeep. They are insubordinate, womanizing, mischievous rule-breakers but they soon prove to be excellent combat surgeons. They immediately clash with their new tent mate Frank Burns, who is both a religious man and an inferior, stubborn, inept and incompetent surgeon who, when he causes mistakes, selfishly accuses anyone that is aside him. Hawkeye and Duke pressure Lt. Colonel Henry Blake, the unit CO, to have Burns removed from "their" tent. They also ask him to apply for a specialist thoracic surgeon to be assigned to the 4077th. Their wish is granted when Captain "Trapper" John McIntyre arrives at the 4077th.
Major Margaret Houlihan, the newly assigned chief nurse of the camp, arrives and has a tour of the camp. In the post-op ward, Trapper sees Burns unjustly blame Private Boone, a dim-witted teenage orderly, for a patient's death. Trapper then confronts Burns and punches him in front of Henry and Houlihan who happened to be walking by. Henry planned to make Trapper chief surgeon, but as a result of what happened, Henry advises him to postpone it for one week because if Trapper is named chief surgeon immediately after what Houlihan witnessed, "you'll hear her yelling in Washington [D.C.] Seoul." Later, Houlihan has a brief discussion about Army protocol with Hawkeye while claiming that Burns is a "good" technical and military surgeon, and reprimanding Hawkeye's nickname, calling it inconsistent. Hawkeye develops an immediate dislike for Houlihan as a result, despite being attracted to her, calling her "what we call a regular army clown." Houlihan and Burns then make plans to bring discipline to the M.A.S.H. unit, which they consider to be out of control.
While Henry is away visiting General Hammond at the 325th Evac Hospital, Trapper, now named chief surgeon against Houlihan's wishes, leads the camp in a general abandonment of regulations, and wild partying ensues. Burns and Houlihan are appalled and write a report to the General. They also give in to their repressed passions and the two have sex in Houlihan's tent. Hawkeye, Duke and Trapper quickly discover the tryst and have Cpl. "Radar" O'Reilly place a microphone under their cot and broadcast it over the public address system; everyone hears Houlihan telling Burns to "Kiss my hot lips!", earning her the nickname "Hot Lips". Houlihan and Burns, initially unaware of the mic placed underneath the cot, hear their own voices echo over the PA system when the system starts to draw feedback, forcibly ending the sexual encounter. The following day, Houlihan and Burns become the target of harassment and humiliation by the entire camp; when Hawkeye quietly taunts Burns about the encounter, an angered Burns attacks him. As a result, Burns is sedated, restrained and shipped stateside for psychiatric evaluation, much to the camp's delight.
Father Mulcahy, the camp's chaplain, tells Hawkeye that Walt "Painless" Waldowski, the unit's dentist, has consulted him about a problem. Mulcahy feels unable to divulge any details because Walt confided in him during confession. Waldowski tells Hawkeye that he suffered a "lack of performance" with a visiting nurse and now believes he has latent homosexual tendencies. He wants to commit suicide, and asks advice on a reliable method. Hawkeye, Trapper and Duke suggest that he use the "black capsule", a fictitious fast-acting poison. At a farewell banquet that satirizes The Last Supper, Walt takes the capsule (actually a sleeping pill) and falls asleep in a coffin. Hawkeye persuades Lt. Maria Schneider to spend the night with Walt and cure him of his "problem."
Duke announces that he is partial to blondes, prompting Hawkeye to declare that Duke is attracted to Hot Lips. Duke suggests she isn't a natural blonde; Hawkeye bets $20 that she is, but they have no way to find the truth. They develop an elaborate plan in which Hot Lips is isolated in the showers, and counterweights are used to raise the wall of the shower tent, exposing a nude Hot Lips to the entire camp. The plan works, money is exchanged, and Hot Lips is further ridiculed. Infuriated beyond reason over what happened, Houlihan labels the unit "an insane asylum!" and demands that Blake do something to discipline his surgeons, threatening to resign her commission if he doesn't turn Duke and Hawkeye over to the MP's. Blake, who is in bed with his mistress during this time, refuses to have Hawkeye and Duke arrested and callously dismisses Houlihan's complaint. She then leaves his tent, yelling "My commission!", while sobbing in embarrassment.
Trapper is ordered to proceed to Kokura, Japan, to operate on the GI son of a U.S. Congressman. Seeing an opportunity to play golf, he takes Hawkeye to assist. The two invade the hospital and order the patient into surgery within the hour. An old friend of Hawkeye, "Me Lay" Marston, is their anaesthetist, and they quickly finish the surgery. Due to their previous antics, they are cornered by the MP's and escorted to the hospital's commander, Col. Wallace Merrill, who threatens them with a court-martial. They escape repercussions by reminding Merrill that they just saved the life of the Congressman's son. Later, while relaxing at Dr. Yamachi's New Era Hospital and Whorehouse (where Me Lay moonlights as a doctor), Hawkeye and Trapper are alerted to a Japanese-American baby with a serious medical problem. Taking advantage of their status as medical heroes, they go to the military hospital to operate, but are stopped by Merrill. They incapacitate him, anesthetize him, and then take nude blackmail photos of him with one of the prostitutes.
On a visit to the 4077th, General Hammond suggests that the two units play a "friendly" football game, with some money thrown into a pot to make bets ($5,000 or $6,000). Hawkeye comes up with a plan to win all the money. First, they get Henry to apply for a specific neurosurgeon: Dr. Oliver Harmon Jones, a former professional football player for the San Francisco 49ers. Then, they bet half their money up front and keep the ringer (Jones) out of the first half of the game. During the game, Houlihan uncharacteristically participates as a cheerleader in an effort to fit in. Once the other team has racked up some easy points and become confident enough to offer good odds to bet the rest of the money, the 4077th brings in Jones for the second half. The 325th has their own ringers, however, and the 4077th fights back with illegal injuries and by drugging the 325th's running back. The game comes down to the last play, in which the quarterback (Trapper) returns the ball to the center, who then hides the ball under his jersey and runs into the end zone for the winning touchdown while everyone else chases a phantom ball.
Not long after the football game, Hawkeye and Duke get their discharge orders and begin their journey home - in the same stolen Jeep they arrived in.