A Washington woman and two suburban residents were among the 32 U.S. winners of coveted Rhodes Scholarships announced yesterday.

The three area residents are Karen L. Stevenson, 22, of 1217 Evarts St. NE in Washington; Paul E. Gootenberg of 10805 Clermont Ave., Garrett Park, and Stefan R. Underhill, 22, of 26 Canterbury Sq., Alexandria.

Winners of Rhodes Scholarships study for two or three years at Oxford University in England in a field of their choice. They receive about $8,000 to cover tuition and living costs.

The winners were selected from among about 1,250 applicants, according to William J. Barber, director of the program in this country.

A Phi Beta Kappa at the University of North Carolina at Chapel Hill, Stevenson is captain of the women's varsity track and field team. In her junior year, she was the first woman winner of the Jim Tatum Memorial Award for being the outstanding athlete and in recognition of her involvement in extracurricular activities.

A track team member for three years, Stevenson holds the university record in the women's 400-meter dash and the 60- and 100-meter hurdles.

In 1976, she was an intern at the Palo Alto, Calif., Police Department and worked on community relations and an exambination of services available to the area's elderly. In 1977, she was a summer intern with the DuPont Chemical Co. doing a market analysis as a business intern.

Stevenson plans to study French and Russian literature at Oxford. She said expects to go to law school after completing her Rhodes scholarship.

Underhill is a May 1978 graduate of the University of Virginia, where he studied government, history and English.

"I almost fainted," Underhill said when he learned he was a winner. "I was sure it wasn't going to happen."

A member of the school's Honors Society, Underhill served as vice president of the student body his junior year and as presient his senior year.

Now a paralegal at the Washington law firm of Fulbright and Jaworski, Underhill plans to study jurisprudence at Oxford. He will go to law school upon completion of his scholarship.

A Cub Scout master in the Alexandria area, Underhill lists his outside interests as photography, tennis and swimming.

Gootenberg completed his degree in economic history this year at the University of Chicago and was founder and president of the Organization of Latin American Students at the University of Chicago.

Gootenberg plays the French horn, engjoys exploring caves and says his career goal is to be a university professor. He plans to study economic history at Oxford.

Other Rhodes Scholars announced yesterday were:

From New England, Margaret Vaillancourt of Manchester, N.H., who went to Radcliffe College of Harvard University; Kenneth W. Banta of Brooklyn N.Y., Amherst College; Deborah J. Marvel of Westwood, Mass., Wellesley College and Sara M. Lord of Albany, N.Y., Yale University.

From Middle Atlantic States, William C. Crowley of Short Hills, N.J., Yale; Nicholas A. Ulanov of New York, Princeton University; Glenn A. Fine of Melrose Park, Pa., Harvard; David M. Lodge of Lookout Moutain, Tenn., University of the South, Sewanee, Tenn.; Charles D. Goodgame of Miami, University of Mississippi, and Nancy-Ann E. Min of Rockwood, Tenn., University of Tennessee.

From Great Lakes States, John P. Santos of San Antonio, Tex., University of Notre Dame; Jennifer A. Havercamp of Madison, Ind., College of Wooster in Ohio, and James Der Derian of Milwaukee, McGill University in Montreal.

From Middle West States, Elaine C. Hefty of Valley Falls, Kan., Kansas State University; Michael J. Hopkins of Omaha, Neb.; Northwestern University in Evanston, Ill.; Helen E. Graham of St. Louis, Mo.; Radcliffe; Jon Peacock of Spirit Lake, Iowa, Iowa State University and the Johns Hopkins University Medical School; M. Victoria Kiechel of Mobile, Ala., Yale; Pat M. Baskin Jr. of Midland, Tex. Davidson University in Davidson, N.C.; Jeffrey A. Jackson of El Paso, Tex. Air Force Academy, and James E. Hildreth of Camden, Ark., Harvard.

From Southwestern States, Robert Maloney of Los Angeles, Harvard; Frank H. Allen III of Albuquerque, N.M., University of New Mexico; Zoe D. Kececioglu of Tucson, Ariz., University of Arizona, and Daniel H. Case III of Honolulu, Pinceton.

From Northwestern States, Ruth S. Mazo of Eugene, Ore., Yale; Robin U. Russin of Laramie, Wyo., Harvard; Michael L. Hoffman of Payette, Idaho, Boise State University; and Thomas A. Smith of Boise, Idaho, Cornell University.

The Rhodes Scholarship program was founded in 1903 as a trust from the assets of Cecil J. Rhodes, an explorer, colonial statesman and diamond mine king in South Africa.

Barber, an economics professor at Wesleyan University in Connecticut, said the scholarships are awarded each year to men and woman of "intellectual distinction who exhibit athletic vigor and display qualities of leadership and concern for the public interest."