Work is now under way on the $70 million Hyatt Regency Plaza hotel and office buildings on a 3 1/2-acre site near National Airport in South Arlington.

The development of Airport Plaza Associates will include an 18-story, 615-room Hyatt Regency hotel with a five-story atrium and a connected, adjacent 12-story office building with 134,000 square feet of space. There will be underground parking for 770 cars on the site at 2687 Clark St., a parallel service road east of Jefferson Davis Highway (Route 1).

Designed by Vlastimil Koubek and Associates, the two new buildings are being constructed by the George Hyman Construction Co. The office building is scheduled to be completed next fall, and the hotel opening is set for the spring of 1982.

Permanent financing of $54.9 million was recently arranged for the project by Sonnenblick-Goldman Corp., a mortgage banking firm with an office here.

Airport Plaza Associates, the developing firm, includes Washington investor Kingdon Gould Jr. and his son Kingdon III and also members of the Abram Purtzer family of Chicago. The Purtzers own the Hyatt Hotels Corp., which has 14 other hotels under construction. There is an existing Hyatt Regency on Capitol Hill and another in Rosslyn.

The new hotel and office building will be located near 26th Street and have direct access to National Airport from a point south of Crystal City, where the Charles E. Smith Companies has been a major developer of new office buildings, apartments, a Marriott hotel and shopping area for 15 years. oThere are several other hotels and motels in the rapidly growing Crystal city area along Route 1, west of National Airport.