Atlantic Research Corp., one of the largest privately held companies in the Washington area, is going to offer shares to the public shortly.

The Alexandria company filed a registration statement yesterday with the Securities and Exchange Commission, detailing plans to sell about 500,000 shares in an expected range of $10 to $12 apiece, which would raise up to $6 million.

A group of Wall Street underwriters headed by L. F. Rothschild, Unterberg, Towbin will offer the Atlantic Research stock to the public once the SEC clears the registration filed yesterday.

According to Atlantic Research, the company plans to sell 300,000 shares and use the proceeds to repay some long-term debts.

In addition, some current stockholders and owners of warrants expect to offer 143,642 shares of stock and 60,029 shares upon exercise of warrants. Atlantic Research workers who purchased stock last year under terms of an employe stock plan also will be given an opportunity on new shares. All existing warrants to buy stock will be exercised in connection with the public offering, the registration statement said.

Atlantic Research was organized in Virginia in 1949 and has become one of the leading companies in Washington's expanding research and development business sector. Since World War II, the region's base of R&D, electronics and scientific firms has come to rival that of Northern California and the Boston area.

A recent study for promotion of a Baltimore/Washington "common market" found more R&D dollars spent in the two metropolitan areas than in Massachusetts during 1975 ($225.6 million vs. $148.1 million).

Last year, Atlantic Research's sales exceeded $45 million, compared with $33 million in 1977 and under $28 million the year before that.

The Alexandria firm's profits also have been climbing. Last year, Atlantic Research earned $1.3 million ($1.19 a share) compared with $917,000 (97 cents) in 1977.

In the first three months of 1979, according to yesterday's filing with the SEC, Atlantic Research profits were $354,000 (31 cents) on sales of $12.3 million compared with year-earlier earnings of $281,000 (30 cents, with fewer shares outstanding) and sales of $9.9 million.

Atlantic Research has assets of $23 million, total debts of $14 million, about 1.100 full-time employes and 100 part-time workers. More than 70 employes have master's degrees and 16 hold doctoral degrees. "Future growth and success will depend upon the continued ability of the company to attract and retain such personnel," the registration statement says.

Early business of the firm, which won wide recognition in government and industry, was concentrated in solid propellant rocket motors. Much of its work has been as a subcontractor under various Defense Department programs.

In 1967, Atlantic Research was acquired by Susquehanna Corp., and in 1972, Susquehanna reorganized the Alexandria firm in the wake of problems that adversely affected the parent company. Subsequently, 10 senior officers and employes at Atlantic Research began buying back from Susquehanna the stock of their firm. Susquehanna, in the meantime, moved to Los Angeles and then Denver.

On Dec. 31, 1976, the Atlantic Research officers completed the buy-back in exchange for $4.2 million cash, a $500,000 secured note and a $1 million subordinated note. Five institutions loaned $1 million at that time and they received 320,000 warrants; in the proposed sale of stock to the public, all remaining warrants are to be exercised.

Officers and employes originally bought their Atlantic Research shares at prices ranging from 50 cents to 75 cents a share. Company Chairman Coleman Raphael, now the owner of 28 percent of outstanding shares, would own 236,100 shares (16.4 percent) after the offering, in which he plans to sell 78,700 shares.

Later this week, Atlantic Research will consummate a previously announced two-for-one stock split. After the offering, there will be more than 1.4 million shares outstanding.

Atlantic Research's current business lines include the manufacture and development of data communications test equipment, electromagnetic engineering services, manufacturing of catalytic air purification devices for submarines, commercial printing, custom design and modification of such vehicles as vans, and varied research and development.

The firm has not been paying dividends and under loan agreements, may not make payouts without the lenders' consent.