A man who was described as distraught over the leukemia death of his young son was shot and killed by police last night after holding three hostages for more than 24 hours at the hospital where the boy was treated, officials said.

The hostages, two women and one man, were released unharmed at St. Jude Children's Research Hospital.

Jean Claude Goulet, 40, was killed by police gunfire, police director E. Winslow Chapman said.

Authorities had negotiated around the clock by telephone with Goulet, 40, a welder from Laplace, La., who, armed with a handgun, burst into St. Jude on Thursday and took four people captive in a first-floor, windowless examining room.

A fourth hostage, a 64-year-old doctor, was released in exchange for food a few hours later. The three others were identified as Dr. Paul Bowman, chief of the hospital's leukemia service and the favorite doctor of Goulet's son; Jean Marie Cox, the boy's favorite nurse, and Jo Cummings, a psychologist.

Goulet had prepared a tape about his views on leukemia which he asked to have played on Memphis radio stations. But after the 8-minute tape recorded by police was broadcast, Goulet said he was dissatisfied with its quality, police said.

Goulet's statement was read by Bowman, who said, "Jean feels that research laboratories are being built solely to find a cure and not the cause of leukemia . . . one must find the cause before you can find a cure." The doctor also said Goulet was unhappy because his son was given experimental drugs.

A hospital spokesman said Goulet's son, Robert Michael, 6, died Dec. 27, 1980, after treatment at St. Jude. The hospital was founded 20 years ago by entertainer Danny Thomas, who was in telephone contact with officials during the incident.