A federal grand jury in Alexandria, indicted a Falls Church office supplies salesman yesterday as part of a continuing probe of fraud at the General Services Administration.

The indictment, the first to be returned in Virginia in connection with the GSA investigation, charged Walter C. Lina, 35, with conspiracy to defraud the government and bribery of two GSA supply store managers. The store managers allegedly cooperated with Lina in a scheme by which Lina's firm was paid for goods never delivered to the GSA.

Lina, who worked for W. H. Brewton & Sons Inc. in Georgetown, is alleged to have given one of the GSA store managers, Charles J. Allen, three citizens band radios and $1,500 in cash to cooperate with the scheme. A second store manager, Manuel M. Cumes, and other GSA employes are alleged to have received household appliances, carpeting and cash.

Both Allen and Cumes already have pleaded guilty and been convicted for their part in the alleged arrangement with Lina.

Federal prosecutors from Maryland, who will try the Lina case in Alexandria, said yesterday they uncovered the alleged fraud scheme during a two-year probe of 30 federal supply stores in the Maryland, Virginia and District of Columbia region.

They said further indictments in the GSA case can be expected within six to eight weeks.

Assistant U.S. Attorney Daniel M. Clements said yesterday the new scrutiny of GSA and that agency's own tightened procurement operations have resulted in a saving of about $1.3 million to the government. GSA supply stores used to bill other agencies $2.5 million a month for supplies, compared to $1.2 million now, he said.

Yesterday's indictment brings the total number of persons indicted in the probe to 48, including 19, or roughly two-thirds, of GSA's store managers. Forty-two have been convicted and five are awaiting trial.

If convicted, Lina could be fined up to $20,000 and face a prison sentence of up to 15 years.