The older cities of the Northeast and Midwest, excepting New York and Chicago, will soon be receiving a smaller proportionate share of the federal housing pie while the suburbs and cities of the South and West will get a larger share, according to a recently released report by the Brookings Institution.

The study, commissioned by the Department of Housing and Urban Development, urges a shift in the way community needs are determined. Instead of basing grants solely on population and poverty, they should also be based on the city's age, using pre-1939 housing as the criterion, the report suggests.

In analyzing the first year of the Community Development Block Program, the Brookings team headed by Richard P. Nathan, also found that it tends to favor moderate as well as low-income persons - the "something for everyone approach" - that it favors housing rehabilitation in marginal neighborhoods rather than totally new construction in the most lighted inner city areas. The program grants have the effect of helping keep the poorest bunched together rather than spreading them throughout the community, it was noted.

The block grant program, under which lamp sums are given to communities without their specific use being dictated by Washington, was passed by Congress in 1974 and is due to expire this fall. Representatives of those cities that stand to get a decreased share are calling for a change in the need formula as well.

Of the 14 worst-off cities in the nation, 12 are now due to receive less in 1980 than they did in the 1968-72 period, the study noted. The cities will not receive fewer dollars, it added - they will just not continue to receive the disproportionately high share of funds they did under previous HUD programs, like urban renewal and model cities.

Newark, the most blighted of all in Brookings index, will get a 52.2 per cent smaller share in 1980. Others include Cleveland; Hartford, Conn.; Baltimore, (which is receiving 44.2 per cent less); St. Louis; Atlanta; Rochester, N.Y.; Gary, Ind.; Dayton, Ohio; Detroit; Richmond, Va., (51.9 per cent less), and Philadelphia.

The only exceptions are New York, which will get 50.5 per cent more, and Chicago, which stands to get 45.5 per cent more as a result of having populations in excess of one million.

The main reason the other cities will get a smaller share is that they now have fewer people than prior to 1970. Only Richmond, with a population increase of 13.4 per cent, and Atlanta, with an increase of 2 per cent, are on the losers list.

As their share of the total pie - now worth $3.2 billion a year - shrinks, the share for areas with increasing population, poverty and overcrowded housing gets larger. These areas tend to be in the South and West, along with suburbs of big cities.

The biggest gainers, ironically, are those lowest on the hardship index. Omaha, Neb., for instance, stands to get a 637.3 per cent increase in its share of federal funds. Projections to 1980 indicate losses in the aggregate of more than $300 million, with the central cities' share of total funds declining from 71.8 per cent to 42.2 per cent.