Walter E. Washington and Sterling Tucker no longer hold elected office in the nation's capital, but they do own pieces of embossed metal that would be the envy of most of their fellow citizens.

The items are license plates, which every auto in the city must have, but Washington's and Tucker's are different. Washington's tag bears the legend, "First Elected Mayor" and Tucker's, "First Elected City Council Chairman."

Yesterday D.C. Mayor Marion Barry, who succeeded Washington, issued a partial listing of the low number license tags, traditionally viewed as indicative of the political pecking order in the city.

In reassigning some of the tags this year, some of last year's political patrons were either given higher number tags among the 1,250 that are given out by the mayor and the City Council, or not given low number tags at all.

Ben W. Gilbert, Washington's director of municipal planning who has been removed from his post, lost tag number 490 that he had held for 32 years. Washington's special assistant and right-hand man, Joseph P. Yeldell, lost tag 11, but was reassigned 490. His wife, Gladys, lost tag number 35 and did not receive a low numbered tag at all.