VSE Corp. of Alexandria, a diversified engineering and graphic communications firm, is making an $8.8 million public stock offering of 502,000 shares at $17.50 per share. At the time of the filing April 21 with the Securities and Exchange Commission, VSE stock was trading over the counter at $15.50.

The company was founded in 1959 to aid the government in reducing the cost and improving the reliability of various types of equipment. Government contracts now account for 93 percent of VSE's revenues, which amounted to $50.6 million last year. Net operating income was $1.6 million, ($1.11 per share), down 28 percent from 1981, although income from continuing operations that year, without the $1.2 million sale of a building, was just $881,000.

VSE has assets of $27 million, working capital of $7.3 million, and lines of credit totaling $10.3 million. The company is composed of VSE, formerly known as Value Engineering; D&P, a graphic communications firm; MetCap, a small business investment compay; and Starr, a property management company.

Net proceeds will be used for working capital and to retire some of its $8.3 million in long-term debt. Part will finance increases in accounts receivable from contracting activities and for facilities and equipment purchases for D&P. Another $1 million will be used as capital for MetCap or to make investments which MetCap is not eligible to make.

Of the shares offered, 22,000 are being sold by VSE Chairman and President John B. Toomey, who will still own 41.9 percent of the company. The underwriters are Advest Inc. in New York and Wachtel & Co. Inc. of Washington.