St. Elizabeths Hospital, the mammoth Southeast Washington institution for the mentally ill, has a rich and distinguished history but an uncertain future.

For 18 years, the federal government has been trying to get out of the business of operating St. Elizabeths. The Reagan administration and the National Institute of Mental Health, the hospital's fourth and most recent federal overseer, now think that within a year and a half they will have a private corporation created to run the hospital.

Under legislation to be submitted to Congress this spring, federal funding of the institution would diminish to nothing over the next 10 years while the District of Columbia assumes more and more responsibility for operating a hospital where 90 percent of the 1,871 patients are city residents.

Dr. William H. Dobbs, the 57-year-old superintendent of the hospital, said he thinks the current proposal "has a better chance" to be approved than previous plans. He said he is optimistic because "this is the first plan that's been jointly worked out with the District and the first plan which puts us both together" for at least a decade in running the hospital and the city's mental health, drug abuse and alcoholic treatment programs.

But James A. Buford, director of the city's Department of Human Services, said he is somewhat pessimistic about the chances for creation of a corporation to run the hospital, because the Reagan administration now is proposing the creation of a private corporation to run the hospital, rather than the public corporation that city and federal officials had reached basic agreement on during the Carter administration. The federal government would have continued to heavily finance the public corporation.

Buford said the impending proposal, under which the federal government would end its financial support for the hospital by 1993, is "too drastic in light of the city's financial constraints."

Dr. Herbert Pardes, director of the National Institute of Mental Health, said he is "a bit more optimistic" now than in past years about chances for creation of a corporation to run the hospital, but he admitted that the issue of the federal government's phaseout of its financial support over the next 10 years "would be a sticking point."

St. Elizabeths was opened in 1855, largely at the behest of Dorothea Lynde Dix, the 19th century crusader for the mentally ill who badgered Congress into establishing the facility. For 61 years it was officially known as "Government Hospital for the Insane."

But the shift toward the name St. Elizabeths emerged during the Civil War. Injured soldiers recuperating at the hospital preferred not to write home that they were staying in a hospital for the insane. They instead said they were staying at St. Elizabeths Hospital, named after the tract of land where the institution was built.

The name stuck and Congress made it official a half century later, mistakenly, as it turned out, without the apostrophe in "Elizabeths."

Thousands of patents have been treated at the hospital, but probably the most famous was Ezra Pound, the acclaimed poet who was charged with treason for his pro-Fascist radio broadcasts during World War II. According to an account published last year, Pound was saved in 1945 from being tried on the treason charges by the hospital's superintendent, Dr. Winfred Overholser Sr., who was able to "singlehandedly" commit him.

Pound stayed 13 years, living in high style, while writing three books and visiting with many of the literary giants of the 20th century, according to Dr. E. Fuller Torrey, a staff doctor at the hospital. Torrey claims that more than 40 psychiatrists decided that the poet was sane and fit for trial and described Overholser's actions as "one of the earliest and most flagrant examples of the ongoing abuse of psychiatry in the American criminal justice system." Pound was released in 1958 and died in 1972 in Italy.