Crime has grown at a rapid rate in all of America's cities, regardless of their size, location, minority populations or whether they are gaining or losing population.

It no longer is a local problem to be dealt with on a local level but is a nationwide phenomenon growing at almost the same rate from Long Island to Los Angeles, beyond the control of local governments.

These are some of the surprising conclusions of a 3 1/2-year study done for the Justice Department by Northwestern University's Center for Urban Affairs and Policy Research.

"The growth of crime appears to be the result of fundamental changes in the life styles of Americans," write Drs. Herbert Jacob and Robert L. Lineberry, who conducted the $923,000 study for the National Institute of Justice. "It is the result of greater affluence which made more valuable goods available for theft, a condition aggravated by the greater propensity of Americans to leave goods unguarded in empty homes and expose themselves to dangerous situations in traveling around their cities.

"It is also the consequence," Jacob and Lineberry go on, "of there being a larger pool of potential offenders for reasons not well understood by criminologists."

The result of all this, the two political scientists say, is that "crime has surged everywhere in the U.S. regardless of local efforts to stem the flood tide. Whether local officials engaged in herculean efforts or none at all, the crime wave affected their community."

The Northwestern study covers the 31 years from 1948 through 1978 and involves 396 cities, every city in the country with more than 50,000 residents. In-depth studies were done of 10 cities, those with declining populations like Newark, Philadelphia and Boston, booming dynamos like Phoenix, Houston and San Jose, distressed cities like Atlanta and Oakland and relatively well-off cities like Indianapolis and Minneapolis.

Jacob and Lineberry say their study shows a remarkably similar rise in crime rates for cities that bear no resemblance to each other: "Both the Newarks and the Houstons of the United States experienced substantial rises in their reported crime rates. Those increases, moreover, occurred at about the same time and with the same velocity for all kinds of cities."

All 10 cities studied in depth suffered huge increases in their crime rates over the three decades covered. Newark suffered the most, a sevenfold increase in property crime and an elevenfold rise in violent crime. But the thriving cities of San Jose and Phoenix saw property crime more than double and violent crime more than quadruple.

Jacob and Lineberry downplay the role of race in the rise of crime but do not dismiss it.

"Cities which have large fractions of their population that are non-white generally have higher rates for violent crimes," the two political scientists say. "This relationship is much stronger than the relationship between the size of the non-white population and the property crime rate."

Jacob and Lineberry also downplay the roles that age and poverty play in the rising crime rate.

On youth: "At no time did the proportion of the youthful population account for as much as 5 percent of the variance in either violent or property crime rates." On poverty: "The number of poor people in a city is only marginally related to either property or violent crime.