American university students, who once shunned Soviet studies as too boring or difficult, have begun to pour into Russian-language and related courses in the wake of new U.S.-Soviet tensions, Soviet leadership changes and a surge of foundation grants, according to educators across the country.

Enrollment in first year Russian at Stanford, the recent beneficiary of a $1 million Rockefeller Foundation grant for Soviet studies, jumped from 30 to 50 students this year, and the number of students taking 19th century Russian literature doubled. Harvard had to add an extra section to its summer Russian course.

George Washington University will have 24 graduate students in Russian and east European studies this coming year, compared with six in 1982-83.

"I have the feeling we have really turned the corner after a long period of decline," said Dorothy Atkinson, executive director of the American Association for the Advancement of Slavic Studies based here. At Columbia University, Soviet studies administrator Jonathan E. Sanders said student inquiries poured in so heavily that "we stopped counting letters and started weighing them--we've had over 20 pounds."

Government and university officials have complained in recent years of a critical shortage in Russian-speaking Soviet experts in the United States. Some professors suggest that an apparent worsening of Soviet-American relations has helped catch student attention.

"If you see the world as two great camps poised against each other, as the Reagan administration invites us to do," said Stanford Slavic languages and literatures department chairman William M. Todd III, "then instead of talking about another foreign country, the Soviet Union looms as the foreign country."

Atkinson, a Stanford faculty expert on early 20th century Russian social and economic history, said the upsurge appeared to reflect a natural shift in academic fashions, as well as heightened interest growing out of the death of Soviet leader Leonid I. Brezhnev and the rise of his successor, Yuri V. Andropov. But most campus officials agree that the most important stimulant has been a sudden influx of private funds for Soviet research. Last year former U.S. ambassador to the Soviet Union W. Averell Harriman gave a $10 million endowment to Columbia's Russian research center, now known as the W. Averell Harriman Institute for Advanced Study of the Soviet Union.

The Roland and Gladys Harriman Foundation, named for the former ambassador's brother and sister-in-law, gave an additional $1.5 million to endow a faculty chair for the study of the Soviet economy.

Harvard announced a $5 million fund-raising campaign for its Russian Research Center in May. It was launched with a speech by Arthur A. Hartman, U.S. ambassador to the Soviet Union.

Hartman said Soviet scholarship in the United States had been declining for more than a decade, and "with the billions we spend on defense, we could at least do something for our basic knowledge of these people and their policies."

The Rockefeller Foundation recently awarded $1 million for a joint program on Soviet international behavior at Stanford and the University of California at Berkeley. Both houses of Congress are considering a bill that would create a $50 million national endowment. The interest would pay for grants to individuals and institutions studying the Soviet Union.

Soviet studies have been traditionally strong at Stanford. But student interest here declined after the peak post-Sputnik years of the late 1950s and early 1960s. Todd said efforts during that era to introduce Russian-language courses in American high schools also have languished.

College and high school language programs suffered a severe blow when many major universities, including Stanford and the University of California, eliminated their foreign language requirements in the late 1960s.

Both Stanford and Berkeley have now revived the language requirement, Todd said, "although its still very watered down." To be graduated, Todd said, Stanford students must have passed three years of a language in high school, one year of a language at Stanford or pass a proficiency test. Although officials at several universities, including Georgetown and Maryland, reported an increase in students taking Russian and Soviet studies courses, the quality of the newcomers appeared to differ.

Patricia Chaput, assistant professor of Slavic language and literature at Harvard, said many of the unexpected overflow into her intensive Russian-language course this summer had trouble keeping up.

At the University of Michigan, however, student services assistant Gloria Bennish said twice as many graduate students as usual were admitted to the Russian and east European studies program because their academic records were so good.

"It was impossible to turn some of these people down," she said.

Sanders, assistant director of Columbia's Harriman Institute, said new research funds would be used to lure good faculty and create new study opportunities for graduate students.

This, he said, would help draw talented students who otherwise see little use in pursuing their love of Russian language and literature.

"Dostoevski and Tolstoy are still great recruiting agents," Sanders said.