Sterling A. Brown, a poet and former professor of literature who helped to establish Afro-American literary criticism and who taught many of the nation's black scholars and writers, died of leukemia on Jan. 13 at the Heritage Health Care Center in Takoma Park, Md. He was 87 years old and lived in Washington.

Robert G. O'Meally, a visiting professor of literature at Barnard College, said yesterday that three works by Professor Brown helped lay the cornerstone of Afro-American literary criticism. A 1931 essay, ''Negro Characters Seen by White Authors,'' deals with the history of black stereotypes in literature and drama. The other works are ''The Negro in American Fiction'' and ''Negro Poetry and Drama,'' both books published in 1937.

With Arthur P. Davis and Ulysses Lee, Professor Brown edited the book ''The Negro Caravan'' (1941), which Professor O'Meally called the ''first comprehensive anthology of African-American writing,'' including every form from slave narratives to contemporary material. A Master's From Harvard

Professor Brown regarded himself primarily as a teacher. It became his occupation in 1923 when armed with his bachelor's degree from Williams College - where he was a Phi Beta Kappa - and a master's degree from Harvard, he went to work at the Virginia Seminary in Lynchburg.

He also taught at Lincoln University in Jefferson City, Mo., and at Fisk University in Nashville before he went to Howard University in Washington in 1926. Over the years, he was visiting professor on many campuses, among them Vassar and Wesleyan, the New School for Social Research, the University of Illinois and the University of Minnesota. He retired in 1969.

Some of Professor Brown's distinguished students at Howard University were the writers Amiri Baraka, Toni Morrison, Michael Thelwell and Paula Giddings, Judge Spottswood W. Robinson 3d of Federal appeals court in Washington, the psychologist Dr. Kenneth B. Clark and the actor Ossie Davis. Charles Cobb, a former student who writes for National Geographic magazine, recalls Professor Brown going with students to U Street, a main stem of Washington's black community, ''to drink some bourbon and talk about the life and language of the street.'' Gave Prizes to Students

Professor Brown introduced Howard's first course in Afro-American literature, said Professor O'Meally, and secretly gave prizes to students who borrowed the most books from the university library, who enrolled in the most English courses and who garnered the highest grade-point averages.

His poetry is included in most collections of Afro-American writing. His own collections are ''Southern Road,'' ''The Last Ride of Wild Bill'' and ''The Collected Poems by Sterling A. Brown.''

''His poetry reflects the innovative impulse of contemporary verse as well as the toughness, humor and protest of black American folklore,'' Professor O'Meally wrote in his annotated bibliography in ''The Collected Poems of Sterling A. Brown.''

In his introduction to the book, Prof. Sterling Stuckey of Northwestern University wrote that the poet used ''the great body of Negro music, of the spirituals, blues, jazz and work songs'' to ''extend, not reflect meanings.''

Professor Brown was born in Washington on May 1, 1901. His father, Sterling Nelson Brown, was a minister, a member of the Board of Education of the District of Columbia and a professor of religion at Howard University.

Professor Brown was married for 52 years to Daisy Turnbull Brown, who died in 1979. He is survived by a son, John L. Dennis of Silver Spring, Md., and a sister, Elsie B. Smith of Landover Hills, Md.


By C. GERALD FRASER
Published: January 17, 1989 NY Times