Foreign investment in the United States, which grew nealy 300 percent in the last decade, should be channeled to help distressed areas that suffer high unemployment and declining tax bases, a new study recommends.

The study, prepared for the Department of Housing and Urban Development, urged new incentives, including possible tax breaks, to entice foreign investors to older, economically lagging regions.

"Most newly constructed foreign-owned plants are being located in the Southeast and Far West, growing areas of this nation," said the study, which was made by Analytic Sciences Corp., A virginia company. "States with economic problems have had less success in attracting foreign investments in recent years than earlier years."

Robert Embry, HUB assistant secretary for community planning and development, said the department has yet to decide which recommendations it will pursue. Foreign investment is not the key solution to distressed localities. There is no one "obvious solution," he said.

Other points of the study:

Southeastern cities and states have been the most sophisticated in developing incentives to lure foreign investment.

U.S. offices of foreign banks account for 14 percent of all commerical and industrial loans in the nation; foreign bank assets increased for $23 billion in 1972 to $95 billion in 1978.

Real estate purchases by foreign investors have done little to revitalize distressed localities; most purchases are in highly desirable locations.

Foreign affiliates employ at least 2 percent of the U.S. work force and nearly 20 percent in the petroleum industry.

However, trade by foreign affiliates contributes significantly to the nation's trade deficit.

The study for HUD did not delve deeply into OPEC's investments.

In concentrating on distressed areas, the study recommended:

Creation of a national broker service to bring together places seeking new investment with foreign corporations.

Greater coordination of existing federal grant programs with efforts to attract foreign investment.

Federal tax incentives to improve distressed areas' abilities to attract foreign investment;

Incentives to banks to assist foreignn investors in distressed areas.