The 'distress' index: which of America's best-loved cities are worst off?

For decades, American cities have been sending up distress signals.

And for decades, federal and state governments have been devising expensive programs to address urban problems.

The results are discouraging - to put it mildly.

* Urban decline is still widespread - and a further dwindling of city populations in the near future appears to be irreversible.

* A number of cities are increasingly unable to provide such specific social services as police protection, education, and waste disposal - especially older cities in the Northeast and Midwest.

* Some of the nation's best-loved and most-visited cities - Atlanta, Boston, Philadelphia, St. Louis - occupy the worst slots on the ''distress and decline'' list.

* Solutions to urban difficulties would require some politically unpopular moves: federal aid that targets individuals rather than employers, reduction of tax advantages for individual homeowners, and prohibition of local rent controls , to name a few.

This sobering report card on urban America - described by its sponsors as ''perhaps the most comprehensive analysis of urban decline ever prepared in this country'' - comes in the form of a book-length study recently published by the highly regarded Brookings Institution, a Washington-based research organization.

The authors (Katharine L. Bradbury of the Federal Reserve Bank of Boston, Anthony Downs of the Brookings Institution, and Prof. Kenneth A. Small of Princeton University) spent four years on the book. They analyzed data gathered between 1960 and 1975 on the 121 American cities which in 1970 had populations over 100,000 and were the leading cities in their metropolitan areas.

''A lot of what they say is right,'' says H. James Brown, director of the Joint Center for Urban Studies of Massachusetts Institute of Technology and Harvard University. However, he notes that, like most quality-of-city-life studies, it ''suffers from trying to add apples and oranges'' in some places.

The thrust of the report, however, is scholarly and statistical. City ''distress'' measures five variables: unemployment rate, violent crime rate, percent of population at or below the poverty level, percent of housing built before 1940, and the difference in tax rate between the city and its suburbs. City ''decline'' charts trends such as changes in unemployment, crime rate, city debt burden, and per capita income.

Measuring the disparity between such figures for cities and those for surrounding metropolitan areas (where conditions are frequently better), the authors produced an index to rank the cities.

Those rankings include some surprises. Atlanta, generally thought of as a thriving Sunbelt city, ranks down with Detroit, Newark, and Gary, Ind., on the decline chart. And Boston, in spite of its astonishing building boom and floods of tourists, came in at the very bottom - below Cleveland and Paterson, N.J.

Among cities that are still growing, -Miami proved the most distressed, while Las Vegas was least capable of performing specific social functions needed by its residents. Surprising, too, are the cities at the top: Hampton and Virginia Beach in Virginia, Torrance and Fremont in California, and Parma, Ohio.

In general, the report confirms the frost-belt-to-Sunbelt slide. One factor common to almost all growing cities: a warm January temperature.

But the overall picture, admits Ms. Bradbury, is ''bleak.'' ''A lot of what has happened to cities is the result of upgrading processes,'' she says, explaining that the flight to the suburbs reflects the increasing affluence of those who go. But that withdrawal has left behind those who cannot afford to move. The report's top priority is resolving the plight of the inner-city poor.

The authors call for a voucher system (similar in theory to the food stamp program) to help qualifying individuals obtain education, jobs, and transportation. But even that, they recognize, would ''probably not be effective at attacking the problems of concentrated poverty resulting from widespread socioeconomic and racial segregation in metropolitan areas.'' The reason: ''Such segregation is supported by institutional arrangements that benefit a majority of metropolitan-area citizens.''

Officials from cities with poor ratings - Boston and Cleveland in particular - take strong issue with the report, noting that the numbers are out of date. ''There is something to that,'' Professor Small admits, although he notes that, except for changes in unemployment levels, most of the conditions measured have not shifted very much. Harvard's Professor Brown agrees. ''For all of the screaming about change,'' he says, ''the world changes pretty slowly.''

Are conditions improving under the Reagan administration? ''I would have to say we're going backwards,'' Professor Small told the Monitor. He faults New Federalism for shifting programs, ''especially those that are distributional,'' from federal to local levels.