`Trying to keep my kids fed and off the street. Please help.'

IT is early on a cloudless spring afternoon. Outside a Union Square airline office a young mother, simply but neatly dressed in slacks and a yellow T-shirt, is sitting quietly on the sidewalk with her two small children. In front of her a neatly printed cardboard sign reads: ``Trying to keep my kids fed and off the street. Please help. Thank you.''

A well-dressed, gray-haired woman walking past the little family pauses, and her eyes dart anxiously to the children, a one-year-old boy and a two-year-old girl. Opening her handbag, she pulls out a dollar bill and places it in a tin can next to the sign.

``Thank you very much,'' the mother says as the woman hurries off. She retrieves the bottle her son has tossed out of his stroller and smiles at her daughter scribbling in a coloring book. Then she settles back to watch the parade of people and upscale shopping bags - Saks, I.Magnin, Neiman-Marcus - passing by her urban campsite. Eleven dollars down, $12 to go, to pay another night's rent at the shabby hotel the family calls home.

Panhandlers, prostitutes, and pushers have long been part of the unofficial commerce of big-city streets. But here in San Francisco, another group has joined the ranks of sidewalk solicitors: homeless and low-income mothers and their children. Unable to find steady jobs, affordable housing, or day care, they supplement welfare checks by pleading silently for spare change and goodwill from locals and tourists. Some have husbands or male companions, but many are single mothers who give new meaning and visibility to the phrase ``female-headed household.''

``A lot of mothers do this,'' says the mother, Darlene, who, like others interviewed here, asks that only her first name be used. ``Or else they sit and do nothing until 9 o'clock at night, when they go to the shelter. I've managed to keep my kids out of the shelter this way.''

With a homeless population of at least 10,000, according to estimates by the National Coalition for the Homeless, San Francisco, like other major American cities, must provide limited emergency services for a growing number of homeless families. Some residents complain that begging has become an art form on city streets. And social-service workers are familiar with cases where families asking for money are involved in what one describes as ``a total scam.''

But according to Midge Wilson, executive director of the Bay Area Women's Resource Center, ``The majority of homeless families we work with are seriously trying to change their living situations for the better. They want to get off welfare as quickly as they can. But they have so many roadblocks in their way, like lack of child care, which means they can't go out to job training programs or look for positions. So they get stuck.''

Getting unstuck can be a laborious task. Some parents are struggling with substance abuse and emotional disturbances. Others, with limited education and few marketable skills, are unable to pull together the necessary funds - first and last months' rent, plus security deposit - for an apartment in a city where housing costs are among the highest in the nation. So they search for cheap hotels willing to accept children, then squeeze into tiny, roach-infested rooms with no kitchen or bath. If the day's rent isn't paid by 11 a.m., they may find their few remaining possessions piled outside their door.

``When four people live in one little room, you do a lot of screaming at each other,'' says Larry, an unemployed laborer whose wife, Jeannette, and two small sons are seeking donations on Stockton Street. ``A couple has to love each other a real lot to make it.

``I'll do anything,'' he adds, ``as long as it's money coming in. I want an eight-hour job - get off at 5, come home and relax until 7, then go out for another job until 10 to make more money. But there ain't no jobs.''

Compounding these challenges, Ms. Wilson says, is a sense of isolation. ``The one thing these people have in common is that they don't have a family or friends they can fall back on. That in itself is a hard way to go through life.''

For Darlene, whose parents live in Utah and are unaware of her financial situation, the downward economic spiral began with an unplanned pregnancy. Her children's father also spent much of his meager wages on alcohol. ``I don't drink, so I left,'' she says.

As a professional welder, she hopes eventually to find employment and child care. But in the Tenderloin, the low-income, inner-city neighborhood where she lives, fewer than 200 day-care slots exist for an estimated 2,200 infants and preschoolers, according to Wilson. So for now Darlene and her children, Joshua and Carmel, receive $617 a month in Aid to Families with Dependent Children. She considers the amount generous, but it is not always enough to meet basic needs and keep her from asking for donations at the end of the month.

``I hate doing this because of the smart comments,'' she says. Her unemployed common-law husband, David, a soft-spoken man with a sandy beard, elaborates:

``People say, `You just want money for drugs and drink.' That's not true. Everything we get goes for food, rent, and diapers.

``Sometimes when guys walk by with their girlfriend, they don't say anything, but they jingle the change in their pocket. Or they say, `Can you spare a dollar?'''

In the face of such rudeness, Darlene says, ``I tell people, `Bless you - have a nice day.' But I think, `How would you like to have all your money and cars taken away, and you sit on this corner and see how you like it?'

``You have people who have never had hard times - you can see it in their faces. But they have the nerve to criticize someone who's not a prostitute, who's not spending it on drugs. I've also had women wearing fur coats come up and look at Joshua and say, `Oh, what a pretty baby,' and walk on by.''

Other mothers report similar insensitivity. ``Yesterday I had somebody tell me I should put my baby up for adoption,'' says Dedie, holding her eight-month-old son as she sits outside I.Magnin. ``I'm not going to give up the only thing I've got left. He's my whole life. But people walk by and say, `Look at that - how disgusting.' How am I supposed to feel? I don't like being out here any more than they like seeing me out here.''

Ironically, in 1983, when her own life was still stable, Dedie worked as a spokeswoman for a local homeless caucus. ``Now I can't even get the caucus to listen to me. Programs just don't have the funding to help everyone.''

Those strained resources reflect both the growing size and diverse needs of the homeless.

``The face of poverty is very different today from what it was,'' says the Rev. Floyd Lotito of the St. Anthony Foundation, which serve the poor.

In a 1930s photograph of people in a nearby food line, he notes, ``Practically all of them were white men with suits and hats.'' Now, of the 2,200 people who receive free meals in the St. Anthony Dining Room each day, more than a quarter are women and families.

Some families need only temporary aid. Anna, a friendly, brown-haired woman who is sitting on a bench on Market Street with her two-year-old son and a misspelled sign (``Spare change for food and dipers''), explains that this is only her second time on the street. ``Tommy's father is waiting for a job as a city bus driver, and as soon as that comes through we'll be OK.''

Not all the women seeking money on the sidewalk are welfare recipients. Some see welfare as a trap, because, unlike begging, it could become tolerable.

``If we got assistance, my husband wouldn't work,'' says Margaret, a mother of four young children, who is sitting on a blue crate near Macy's, a dark braid trailing down the front of her hooded jacket. ``It's very easy to get help in this town, but it's not always a good choice.''

Holding her 17-month-old daughter and a sign written on the back of a Pampers carton, she adds, ``I've had a few women come up to me and offer me housecleaning jobs. I've taken them, and the women have let me bring the baby along. I've also had a few job offers for my husband, and he's taken them.''

Still, most days these stints on the sidewalk serve as a reminder that this is no way to earn a living. Parents struggle with boredom and humiliation. Children chafe at the immobility imposed by a stroller or a mother's lap.

On Darlene's little patch of concrete this particular afternoon, Joshua starts to cry after only an hour, and Carmel follows suit. Naptime. So Darlene packs up her sign and tin can, the baby bottle and crayons, and begins the seven-block walk back to their room, two doors down from a theater featuring ``Live Nude Girls.''

``It's hard, it's hard,'' she says philosophically. ``But we deal with it. That's the only thing you can do. What comes to us, we just deal with it.''

Then her voice turns wistful as she adds a final plea to all the nameless passers-by who have ever scorned her presence and her plight. ``People shouldn't pass judgment on other people,'' she says. ``People should just give other people a chance.''