While Kremlin-watchers in Washington looked for political and strategic meaning in the recent change of leadership in the Soviet Union, Susan Graham, a waitress in Springfield, searched for something far more personal -- an indication it might mean a reunification with her husband.

Since they were married three years ago today in a civil ceremony at Moscow's Central Wedding Palace, Graham, 26, and her husband Matvey S. Finkel, 34, a Soviet citizen, have been allowed to live together for a total of only four months.

"With the change in leadership in the Soviet Union there has been speculation about changes and a loosening up," said Graham, a tall, soft-spoken woman who works at a Mexican restaurant. "The State Department has advised us to have patience, but after three years it gets hard. We just don't understand why this is happening to us. We are simply two people who want to live together."

Graham is one of about 15 Americans married to Soviet citizens whose attempts to live together have been stymied either because the Soviet Union has not allowed its citizens to emigrate or have denied residence rights to their American spouses, according to the State Department. Most of the Soviet citizens, like Finkel, have never been active in political opposition.

Finkel, a metallurgical engineer, has been denied permission to emigrate six times. The authorities cite his military background as the reason for the denials. Finkel did his compulsory one-year service in the rocket and artillery corps of the Soviet army in 1972-73.

Graham met Finkel when she was a student in Moscow in 1977. She speaks fluent Russian, has a master's degree in translation and interpretation, and says she is not averse to living in Moscow if she were allowed to do so.

The Soviet government has never given Graham a reason for not allowing her to reside with her husband. She was last allowed to visit as a tourist in April of this year, and since then has been denied an entry visa twice.

Preferring to avoid publicity about their case, Graham chose to work quietly with the help of Sen. Henry Jackson (D-Wash.), while her husband did not join other Soviet citizens married to foreigners who went on hunger strikes this year to draw attention to their plight.

"I just could not stand the thought of my husband starving himself to death and we just did not want to believe we had to put it in the newspapers," said Graham. "We were hoping things would work out otherwise."

Jackson, who has lobbied vigorously with the Soviets for a freer emigration policy, made special efforts on Graham's behalf because her home town is Spokane, Wash., said Jackson's special assistant, Dorothy Fosdick. Jackson twice wrote letters to the late Soviet President Leonid Brezhnev on Graham's behalf, Fosdick said.

"It's the kind of case the Russians could handle easily . . . It would not really involve any backing down on the part of the Soviets," Fosdick said. "All they would have to do is let a person out. It would be a terrific signal . . . to show they wanted to get talking with us on bigger issues."

Though cases like Graham's are small in number, they violate the 1975 Helsinki Final Act that stipulated signatory governments would facilitate family reunifications. About 100 Soviet-American marriages take place each year and about 85 percent of the Soviet spouses are given emigration permits on their first application, according to the State Department.

The longest-standing separation is that of Woodford McClellan, a University of Virginia professor whose wife Irina has been denied permission to leave the Soviet Union since 1974. Another local woman, Baltimore nurse Elena Balovlenkov, is separated from her husband, Yuri; after he went on a hunger strike earlier this year, the Soviet government said it would consider allowing him to emigrate sometime after 1985.

Though there is no indication that Finkel's problems are related to his being Jewish, this factor probably does not help his case. Marcia E. Weinberg of the Jewish Community Council of Washington's Soviet Jewry Committee says Jewish emigration from the Soviet Union has dropped from 51,000 in 1979 to 3,000 so far this year since relations between the superpowers have chilled.

A spokesman for the Soviet Embassy who did not want to be named acknowledged that relations between the two countries "affects each and every matter . . . and generally speaking . . . would affect this case as well."

Graham and her husband communicate by mail and telephone, but since the direct-dial system was cut off in Moscow last September in what some analysts regard as a move to stop dissidents' contacts with the West, it is necessary to book a call a week in advance.

"She has a special quality, she is a person of real courage and determination," Fosdick said of Graham. "Finkel has been to the [U.S.] Embassy in Moscow for dinner, he knows the ambassador well. They have shown great tactical wisdom in not confronting the Soviets with a hunger strike."

"It's a very hard way to live, but separation has made our commitment to each other in some way,stronger," said Graham. "There's no question in either of our minds about what ultimately has to be done. We won't stop pursuing our wish to be together until it happens. It's been most difficult on us both emotionally . . . the past six months have been the worst because our expectations have been raised and we feel it's time something happened to bring us together.

"I think at least 50 percent of our problem is poor relations between the U.S. and the Soviet Union. You kind of feel like a victim. All you can say is, 'Why me?' And there really is no answer to that question."