Leonard Atkins, gray and weak, sat silently at his kitchen table this morning as officials, attorneys and an environmentalist wrangled over how best to dig up his yard. "You can do what you like," he said.

Atkin's yard is the priority place to search for the phantom chemicals of Steel Street, toxic somethings that seem to be making people sick around here. It may all be just another chemical dump story, one of thousands of abandoned and forgotten dumps surfacing nationwide, and awaiting cleanup. But there's one problem: four years of tests have failed to locate any chemicals.

Two streets away, Evonda Pounds rocked her fretful 3-year-old daughter and talked about the sick children and dying dogs that started all this. Little Sabrina had a rash this morning, another in the string of illnesses that now preoccupy the neighborhood of small bungalows.

The children have cross-eyes, strange sores that look like burns, bone troubles. Their parents have cancers, tumors on their feet or breathing problems that won't go away.

"It would seem that a health problem due to chemical contamination may be present in the Frayser area," concluded the most recent consultant's report to the Environmental Protection Agency. The same report, issued this week, also found no evidence of hazardous waste disposal and no source of any combination.

"It's a cover-up, that's what I think," said Marvin Davidson, 33, a machinist who has lived in his North Memphis house here for three years. "They've been whitewashing the test results. Nobody is telling the truth, everyone contradicts each other." His children, he said, suffer fevers and swollen limbs when they play outdoors, but recover quickly at their grandmother's house elsewhere in the city.

He and other neighbors watched the city attorney, an EPA official, the Pounds' family lawyer and Leonard Atkins stomp around on the soggy grass between Atkins' muddy garden and the woodpile. Several little white rags fluttered from wires stuck in the ground. Those marked the spot where core samples will be taken to find out why a metal detector, normally used to hunt Civil War relics, shows something buried down there.

One old drum, rusted through, was dug up outside the kitchen window of the house, and it shows traces of chlordane, heptachlor and dieldrin, pesticides banned as cancer-causing in the mid-1970s. Traces of those chemicals and others were also found in the bloodstream of the Pounds' children and in their back yard, especially under the swing set.

But there are only traces, the EPA report says, the kind that might have come from spraying for termites. A previous resident of the Atkins' house said he put three drums in as kind of a primitive septic tank arrangement years ago. Workers were tearing off the fake brick siding today to give the mottled wood underneath another termite treatment.

However, T.H. Rochelle, 59, said he remembered when the whole neighborhood was a swampy piece of bottom and the size of two football fields, with truck access ramps at either side. That was before the houses went up in the mid-1950s.

"In the mornings, we'd see barrels and boxes there, blue and white or orange and black metal drums.We were going to take one for a garbage can once, but we opened it up and it smelled so bad you couldn't get near it," he said.

After it rains, said Rochelle's wife, Lena, the smells sometimes return, "acidly smells that burn your throat." She had had a cancerous lung removed as well as benign tumors on her feet and vocal cords. She tried to give a deposition to the visiting officials today, and everyone moved to her house and her special breathing apparatus when she ran out of breath.

Ben White, pollution control manager for the Memphis-Shelby County Health Department, said many people have told him there never was any chemical dumping in the area.

Aerial photographs taken in 1937, 1947, 1953, and 1960 show no trace of a dump site, he said. There are six chemical companies in a three-mile radius of the neighborhood, and the city knows of four old dump sites elsewhere. The last one was closed in 1970, White said.

The health problems here have not been systematically compared with those of similar groups elsewhere, and may not be any worse, he said, and they have not been fully documented even for the Frayser residence. He has thought of nothing else for two months, ever since a former Health Department worker revived the public controversy with a charge that the county has more than a score of abandoned dumps.

"It's near-hysteria around here, whether there's any chemicals found or not," he said. "Nothing to date has been found to show that any chemical problem exists."

Evonda Pounds, trim and energetic, has a theory to explain the situation. Her back yard is a morass in the wake of repeated test diggings that began when she first complained that her children were inexplicably sick back in 1976. The yard was flooded again Thursday when a 2-inch rainfall backed up the next door neighbor's storm sewer drain.

The sewer, she said, drains into the Loosahatchie, a stream that flows into the Mississippi, three miles west. Near the Loosahatchie are some chemical plants, on the Wolf River.

EPA officials are trying to clean that one up now. Pounds says she thinks chemicals back up from the Loosahatchie into the storm sewer that runs under the Frayser area. The idea has not been investigated.

Meanwhile, the Pounds family has not written off the old dump theory, and want more tests for their children. Pounds called the Washington embassy of the Soviet Union Thursday on the theory that their scientists "might be more honest. they've got nothing to cover up . . . I wouldn't trust any of these testers here anymore, ever."