About two years ago, Suzanne Riordan was a single mother with a four-month-old baby and no place to live. On welfare and unable to afford housing in the high-rent Santa Barbara area, she lived in her van for a month and lived with friends for two- to three-week periods during the next eight months.
''I could only afford to share an apartment, but it was hard to find someone who was willing to live with a child,'' she says. ''It was a very frustrating experience.''
One day ''it occurred to me if we could get single parents together we could help each other. I wondered how many (single parents) there were out there and how many were struggling for housing.''
She ran a small advertisement encouraging single parents to contact her if they were interested in shared housing.
''I was deluged with responses,'' she says. Soon afterward, with funds from a private donor, Ms. Riordan launched the Single Parent Alliance to help single parents and their children team up in shared-living arrangements.
So far the organization has helped about 1,000 parents and their children find affordable living situations with other single parents. About 90 percent of the clients are women.
''Many of these women were middle class when they were married and now they are poor. Many of them have college degrees,'' says Ms. Riordan.
The Single Parent Alliance is among several organizations around the country that help match single parents of the same sex in shared-living arrangements. Directors of such programs say sharing a house or an apartment can help defray living costs while providing both the adults and children with companionship and a supportive atmosphere during times of transition. In some cases the parents are able to stagger their work schedules so one parent can be home with the children. They may also split transportation costs by sharing a car.
''In a good match parents can cut costs across the board,'' says Judy Fowler, director of the Shared Housing Project sponsored by Catholic Social Services in San Jose, Calif. ''This puts them in a more secure position to be able to move on to something else, perhaps after getting job training or finding a new job. Often moving out of a match is a positive thing, not because the relationship didn't work.''
Ms. Fowler estimates most housemate matches arranged by the Shared Housing Project last from three to 18 months. Most of the single parents are women with incomes of $9,000 to $10,000, but men are increasingly seeking help as more fathers gain custody of their children. From June 1983 to June 1984, the Shared Housing Project housed about 500 families.
Nationally, Census Bureau figures show the numbers of single-parent households have risen steadily since the early 1970s. Currently there are more than 6.5 million, the vast majority headed by women. These figures do not account for single parents living with relatives or friends or those in shelters.
Women with children may face discrimination from landlords who prefer to rent to single professionals or married couples with two incomes. Single women with small babies may not want to work right away, and for mothers who do work, child-care costs can eat up a substantial portion of their paycheck.
Myra Contreras, a single mother with a 11/2-year-old son, was only able to afford a studio apartment in Santa Barbara, but she found landlords would not rent a studio to two people.
Last July, she and her son, Christian, teamed up with another single mother, Sue Beverage, and her 13-year-old daughter, Dana. They now share a three-bedroom apartment. Ms. Contreras is able to stay at home with her son and Dana helps watch Christian.
''It's nice to have the companionship,'' she says. ''The good thing is you can give each other moral support. It's really nice to have someone who is in the same situation - someone as a single parent - you can relate to.''
Kathryn Sears, a mother with two young children at home, is also happy with her house-sharing arrangement. Last February, she found it necessary to rent out a room to another mother and her child in order to afford payments on their four-bedroom San Jose home.
''I'm really pleased with this because it allows my children to remain in their own environment,'' says Ms. Sears, who works as a bank teller.
Last month a third mother with a child joined the Sears household, which now includes four children ranging in age from 3 to 71/2.
''They're all basically easygoing kids,'' Ms. Sears says. ''They have their ups and downs, but generally they get along well.''
The mothers trade off responsibilities such as picking children up from day care or watching children when they come home from school. They also share the housecleaning and other chores.
''I couldn't ask for two better roommates,'' Ms. Sears says.
Some of the challenges facing single-parent housemates are similar to those of other roommate situations, such as establishing ground rules for guests, dividing responsibilities for household chores, and learning to live together in close quarters.
''When a parent is desperate (she) may not ask any questions before moving into a shared arrangement,'' says Ms. Riordan of the Single Parent Alliance. ''This can make for problems down the line.''
''We encourage a written or verbal agreement outlining the expectations of both parties,'' says Vernell Watts, coordinator of Operation Match sponsored by the Montgomery Housing Opportunities Commission. Operation Match has nine offices in the Washington, D.C., metropolitan area.
''We encourage single parents with children to sit down and talk about the needs of the child and the atmosphere they prefer to live in,'' she says.
Parents sharing a home also find they need to decide who will have authority to discipline each other's children and to agree on basic rules for behavior.
One benefit for children is ''they don't have to come home to an empty house, '' says Ms. Riordan. With another adult in the household, parents have more freedom to slip away for a quick errand or to accept a spontaneous invitation to dinner or a movie.
''It's closer to a family environment,'' she says. ''It's much more fun.''
Individuals interested in homesharing may send for a helpful resource guide called, ''Is Homesharing For You? A Self-Help Guide for Homeowners and Renters.'' For a copy, write The Shared Housing Resource Center Inc., 6344 Greene Street, Philadelphia, Pa. 19144.