Homeowners and tenants strapped by inflation are creating a huge, undercover rental housing market in suburban and city single-family neighborhoods across the country.

Owners are subdividing their homes -- often illegally -- in order to meet rapidly rising utility, property tax and maintenance costs.

The rental "apartments" thus produced are carved out of areas such as recreation rooms, the lowest floors in split-levels or the third floors and attics of larger homes. The new dwellings range from tiny 250-square-foot efficiencies with back entrances, to two- and three-bedroom chunks of single-family homes.

Almost always those apartments are rented informally and without professional real estate help, and almost carry modest rents for the area. Typically they violate local zoning ordinances, although more suburbs and cities are beginning to allow "accessory" units in single-family neighborhoods.

The size of the underground rental market nationwide has only recently begun to be documented, according to Dr. George Sternlieb, director of the Center for Urban Policy Research in New Brunswick, N.J.

"What we're coming up with is far bigger than anybody expected -- possibly in the range of 500,000 units nationwide (according to preliminary computer runs of 1980 census data," he said.

Major housing markets -- from New York City to Chicago to the West Coast and Sun Belt cities -- contain tens of thousands of what Sternlieb calls "onesies turned into twosies."

New York's Long Island, for example, has at least 15,000 illegally converted single-family dwellings with interior rental units, according to Lee Koppelman, executive director of the Long Island Regional Planning Board. kSplit-levels in suburbs like Levittown are filled with units rented out to moderate- and lower-income tenants.

When Sternlieb did an intensive housing-market study of suburban Bergen County, N.J., his researchers found nearly twice as many two-household dwellings as there were on the county's official records.

The national economy has been forcing people to "double-up" with family members -- or take in unrelated persons to help pay the mortgage and tax bills -- for the last five years.

Sternlieb says the trend is apparently accelerating, and "has tremendous significance" for housing policy makers at the national and local levels.

On the other hand, if there are as many as 500,000 rental units occupied or avaialable in the underground market, federal government assumptions about the shortage of rental nationally may be unnecessarily alarmist.