Summer, which lies with tantalizing fragile brevity over much of this northerly nation, is now yielding up a crescendo of pure sunny days and lovely warm nights, and Soviets by the hundreds of thousands have jammed the pebble shores of this black Sea resort to rest up for the long winner to come.

They have filled every available space in the dozens of resort hotels, sanitariums and boarding houses, and spilled over onto the narrow beaches, where hundreds of mostly younger Russians have taken up an orderly, seemingly semi-permanent existence of daytime bathing and endless night-time conversation.

City officials believe that there are 600,000 people here now, in a city of 280,000 permanent residents. Some 80,000 visitors are housed in the official sanitariums and hotels but most, called "savages" in Russian, rent separate beds in crowded local apartments and houses via a local rental exchange, or in privately arranged deals out of sight of officials.

For the most part, the Soviets in crowded Sochi take their pleasures wherever they find them - in long, meandering walks along the seaside road, or through well-landscaped parks that stand put attractively even in this semitropical city, with its flowering oleander, palms, Siberian pines, cyprus and tall Lombardi poplars. Or they line up patiently at overworked ice cream kiosks, or wait half an hour or so to get a glass of lukewarm Kvass , a special Russian summer drink, decanted direct from a tank truck drawn up along the seafront.

But for thousands, especially the middle-aged factory workers whose sweat stokes Soviet industry, the real point of the vacation, aside from swimming and sunning, is found within the quiet domain of the special sanitariums, where they can nominally seek a cure for a variety of work retailed ills.

There are dozens of these spas in Sochi, run by the powerful, multimillion-member unions to which Soviet workers belong and watched over by a special central Institute of Spas and Physical Therapy. Here is an aspect of Soviet reality that is effaced on the beaches, dominated as they are by the flashier younger generation, with its eye-catching physiques and bathing gear to match, its insatiable appetite for Western clothes and knowledgeable rock 'n' roll patter.

Virtually every major industry and trade is represented here or in other Black Sea resorts, such as Pitsunda and Yalta. But Sochi is the center, where one can find more than 50 rest homes that specialize in catering to every kind of worker, from metallurgical fabricators and foundrymen, to Aeroflot airline employees, actors and actresses, cab drivers and even journalists and critics.

The sanitariums are not hospitals but they have staffs of doctors and nurses who examine their guests for what ails them and then prescribe cures, usually involving carefully staged amounts of swimming and sunning, exercise, dietetic foods and bathing in the nearby mineral springs. The Soviets have designated Sochi as a center for treatment of cardiovascular ills and nervous disorders. A guest usually spends 24 days at a spa, with two-thirds of the cost paid for by his factory or union, generally as a reward for hard work and political reliability.

To a Westerner, conditioned to look for specific diagnosis and specific prescription, frequently of some kind of drug, the sanitarium approach of ills and cures can be startingly different.Here is Dr. Vladimir N. Sarmakeshev, director of the Metallurgy Sanitarium, a 350-bed showplace to which visiting journalists are frequently taken:

"We don't treat by drugs, we treat by 'natural factors.' We have at our disposal mineral baths, hypnosis, psycho-therapy, conditioning diet." All these will be used in varying degrees to treat either cardiovascular problems or nerves.

"Our treatment is directed to the revival of the human organism," said the doctor, guiding his visitors through numberless massage rooms, showers, baths, sunrooms and alcoves for "galvanic current" treatment of sore backs and aching joints, where sleepy men and women silently took their cures.

At the center of the Sochi spa business is the "Matsesta" mineral springs enterprise a complex of seven buildings set in a narrow valley ringed by steep hills. Every day, an average of 13,000 people make the piligrimage to Matesesta disregarding its distinctly pungent sulfurous air to bathe under the watchful eye of a physician or nurse in the brownish waters that are laced with hydrogen sulfide.

Matsesta is an ancient local word for "firewater," a descriptive that has to do not with its effects on the brain, but rather, on the skin. A bath on from eight to 15 minutes in the water flushes the skin of most caucasians a bright, angry pink, as the skin's capillaires open to rush blood to the surface to combat the heat and irritation of Matsesta. Soviet physicians say that the flushing of the skin draws out poisons and other impurities that could otherwise erode the health. In this regard, the waters are similar to baths of Epsom slas which American doctors sometimes prescribe to reduce the swelling of an infected extremity.

But over the years the use of Matsesta has expanded, and it is now prescribed routinely in a variety of strengths, times and ways to treat a marvelously wide range of ills.

For example, according to Dr. Anatoly F. Golubov, deputy chief physician at the springs, the water can be helpful in the treatment of sleeplessness rheumatism, exzema, swollen joints, back ache, hypertension, bowel malfunctions, gynecological problems, Gum disorders, laryngit is and bronchitis and many other ailments.

Whatever its creative powers, Mateseta is an undeniable potent natural concoction Pumped up from wells as deep a 9,000 feet, it can turn an immersed kopeck from a shiny yellow to a dark gray in a few minutes. Full immersion for a full 15 minutes normally saps the strength of the bather, much as a hot bath might, and nurses customarily help the weakened person to a 20-minute rest on a nearby couch to get strength back before facing the world again. A complete treatment would be up to 14 Matsesta baths spread over 28 days.

The popularity of the mineral spring is growing, according to Golubov, and there are major building programs now under way to double the spa's capacity to 1,070 beds by 1980, the end of the current five-Year Plan. During the height of the season the parking lot in front of the handsome main building is choked with buses and taxis carrying guests to and from the center.

Matsesta is well-known throughout the Soviet Union and revered as something bordering on a national treasure. The mineral springs were specifically dedicated to the use of the entire nation by a Soviet decree signed by Lenin himself, a matter of great local pride and the subject of a handsome stone monuments in the carefully gardened forecourt of the Matsesta spa.

It is impossible to say preceisely how many of the three million visitors to Sochi this year will in fact take the waters at Matsesta, but the statistics from the spa itself hint at a great number. There were 5.78 million "procedures" logged in 1976 and the number will surely increase, just as the number of vacationers has increased dramatically in recent years.

Said Goluboy with obvious pride: "We are 96 to 98 per cent effective in helping cure the diseases that are treated here."