FLAKES of crumbling brick drew the archeologist step by step along the line where the wall of an ancient city of lower Mesopotamia once stood. The trail led to remnants of the south gate, and there on the ground lay a clay fragment bearing cuneiform inscriptions.

One name leaped out from the inscribed symbols: Mashkan.

In that moment of discovery this January, Elizabeth C. Stone, the archeologist, knew she had found and identified one of the oldest lost cities in the cradle of civilization between the Tigris and Euphrates rivers of southern Iraq. It was without doubt the site of Mashkan-shapir, which flourished 4,000 years ago, becoming a capital of the rival power to rising Babylon. But the city had left little trace in history, except for references in the letters and law code of the great Babylonian ruler, Hammurabi.

Dr. Stone, associate professor of archeology at the State University of New York at Stony Brook, and her co-investigator and husband, Paul Zimansky, assistant professor of archeology at Boston University, announced the discovery last month and described its significance in interviews last week. They said that finding the remains of Mashkan-shapir could be one of the major developments in Mesopotamian archeology in more than 40 years.

The site, in the desert about 90 miles southeast of Baghdad, has not been occupied since the city was sacked and burned around 1720 B.C. Most ancient cities were inhabited for thousands of years, with the culture of one era building on top of another. This makes it difficult to separate layers of deposits to understand urban life of any given time. Mashkan-shapir, however, enjoyed one distinct 300-year period as a major trading and manufacturing center of 15,000 people, from about 2050 B.C. until it was sacked.

After aerial photographic surveys and some exploratory digging, Dr. Stone said: ''We have a whole city plan laid out there for us. We know where the canals were, the cemetery, the palace and religious quarters, the manufacturing area and the city wall. A complete, undisturbed city - that's what's really exciting about it as an archeological site.''

Because the city was suddenly abandoned, rather than falling into slow decline, Dr. Stone said, the ruins should include many domestic possessions the fleeing people left behind. The result could be an illuminating picture of daily life among all classes.

Other scholars cheered the news. William Hallow, professor of Assyriology at Yale University, said, ''It's always a happy day in archeology when someone nails down the identification of an ancient city.''

But archeologists doubted that Mashkan-shapir would prove to be as rich a lode as Ebla, an ancient city in Syria whose voluminous archives were uncovered in the 1970's to reveal a previously unknown language. They said that, depending on later findings, the site could rank in importance with Tell Leilan, the second major Mesopotamian find since World War II. In 1985, archeologists discovered that Tell Leilan in northern Mesopotamia had been the seat of a powerful kingdom in the 18th century B.C. and contained a major archive of royal correspondence. It afforded rare glimpses into life beyond the more celebrated cities of southern Mesopotamia, notably Bablyon.

The Mashkan-shapir discovery is already the talk of archeology because it is the rare instance of a site of an ancient city being found and then being identified in one swift stroke. Archeologists must often dig for years before uncovering archives and monuments establishing the city's name and place in history. The identity of the new discovery was determined in the first six weeks of preliminary surveys. A Promising Site

In 1975, Robert McC. Adams, a University of Chicago archeologist who is now secretary of the Smithsonian Institution, noted a scattering of potsherds and other artifacts at the site and so included it in his comprehensive survey of promising places for future exploration. But Dr. Stone and Dr. Zimansky were the first to begin systematic exploration.

Two years ago, they collected fragments of clay figurines and metal objects on the surface there and traced faint discolorations in the sunbaked soil, which betrayed the outlines of buried or eroded brick building foundations.

The archeologists then examined satellite images of geological patterns revealing the course of the Tigris in earlier times and the routes of ancient canals and a branch of the river that had served the city.

Closer aerial examination was hampered by Iraqi military restrictions against using aircraft for photography. But Dr. Zimansky was not deterred. He lofted a kite carrying an automatic camera and soon had pictures revealing all the important building sites, outlines of the city wall and other features that were not immediately apparent from the ground.

Returning to work at the site last December and January, Dr. Stone and Dr. Zimansky dug test trenches with the aerial photographs from the balloons as their guide. Their work was supported by the American Schools of Oriental Research and the National Geographic Society.

Close to a dry riverbed the archeologists uncovered the religious quarter, consisting of mudbrick and baked brick platforms that must have supported temples dedicated to Nergal, the ancient Babylonian god of death, pestilence and other disasters. Elsewhere, model chariots in clay bear emblems portraying Nergal or the scythes with which he performed his work as the original grim reaper. This, then, was clearly a city built in honor of Nergal, as neighboring Ur was the city of Nanna, the moon god.

Other spot excavations located the cemetery, where the dead were buried in huge jars, accompanied by beads, copper amulets, weapons and other personal effects. Pottery and copper-bronze workshops were uncovered. The preliminary survey produced more than 600 artifacts, though there were no indications of valuable metals or jewels. Most Prized Discoveries

But the most prized finds so far are the many fragments of clay cylinders bearing inscriptions in the wedge-shaped Sumerian symbols known as cuneiform. The cylinders were about 12 inches long and 6 inches wide. Most of these, like the one Dr. Stone picked up at the south gate, were apparently commemorative objects placed in the foundation of the city wall.

Indeed, as translated by Piotr Steinkeller, professor of Assyriology at Harvard University, the inscription on each piece began with the same phrase: ''When the great lord, the hero, Nergal, in his overflowing heart verily caused his city Mashkan-shapir to rise and determined to build its wall in a pure place and to expand its dwellings . . . .''

''There's no doubt,'' Dr. Steinkeller said, after examining the inscriptions and confirming Dr. Stone's initial conclusion. ''One couldn't hope for better evidence of the city's identity.''

Scholars had known something of the city's existence from Babylonian documents. But most experts, if they thought much of it at all, had assumed that the site was farther south of ancient Babylon and thus closer to Larsa, Babylon's rival power.

What followed in the inscriptions identified the king, Sin-iddinam of Larsa, who ordered the wall to be built and described how the army was mobilized for the task. The wall was erected about 1850 B.C., a time when the city was growing in stature.

Although nominally ruled by the city-state of Larsa in the south, Mashkan-shapir was becoming a strategic military and economic center on the trade routes between southern Mesopotamia and Assyria in the north and Iran in the east. In the early 18th century B.C., ambassadors from Hammurabi regularly called on Mashkan-shapir and the Babylonians gained control over the southern territory only after defeating that city's forces. Decline of Babylon

Moreover, when Hammurabi's empire began to collapse after his death in 1750 B.C., rebellions in Mashkan-shapir contributed to the decline of Babylon that would last until it regained eminence in the 7th and 6th centuries B.C.

Dr. Stone and Dr. Zimansky plan more mapping and detailed excavations at Mashkan-shapir, beginning early next year. They expect to focus on the presumed site of the palace and temples, where they may be more likely to come upon any surviving archives.

''This is going to be a long-term project,'' Dr. Zimansky said. ''We'd be happy to spend the rest of our lives digging there.''

Map of Iraq showing location of Mashkan-shapir) (NYT) (pg. C10)