BEFORE THE BODIES had been taken away from the site of the crash of an American Airlines DC 10 in Chicago 10 days ago, the nation's small and exclusive group of "air disaster" lawyers received the first inquiries from the shocked relatives of the 274 victims.

Four days after the catastrophe - the first day the courthouse doors were open after the holiday weekend - lawsuits for damages were filed, one in Chicago and one in Los Angeles.

And late on the sixth day after the crash, an investigator for the Illinois attorney disclipinary committee got the first signal that the race for cases was on. A man with the same name as the husband of one crash victim had received several telephone messages that left the number of a prominent Chicago attorney. It was as if someone had paged through the telephone book, matching the names with a list of the dead.

The long, complicated and sometimes ugly process of pinning down the blame and assessing the cost of the country's worst air disaster has begun.

The air disaster lawyers, a tiny fraternity of specialists with unusual expertise in the complexities of aircraft and the law of aviation, will slowly piece together their version of why the crash occurred. With damage awards or settlements virtually guaranteed, legal fees can climb over the million dollar mark.

"There's no doubt about it . . . there's bucks there," said W. Morgan of Morgan Wenzel and McNicholas in Los Angeles.

"You can make a lot of money if everything falls just right. There are lawyers who will make a tremendous amount of money on this case."

John J. Kennelly, 59, the author of a two-volume book on air crash litigation, estimates that damage payments to the families of the crash victims will average $300,000.

Over the past 15 years, as aviation technology gained sophistication and aircraft design became increasingly complicated, air disaster litigation became an art. Only about eight law firms scattered throughout the country take on the massive cases. Within those firms, a handful of high-powered, finely skilled plaintiffs' lawyers virtually monopolize major crash cases wherever they occur worldwide.

Air disaster lawyers consider Kennelly one of their deans. White-haired and unassuming, he has been in the business for 21 years.

Donald W. Madole and his wife Juanita, both are pilots and lawyers with the firm of Speiser Krause and Madole in Washington. Unlike Kennelly, who works as a lone wolf, the Madoles team up on disaster cases.

Donald Madole, who spent years as a lawyer for the Federal Aviation Administration, American Airlines and the Civil Aeronautics Board, will handle the Chicago disaster cases for the firm. He knows the aircraft and the people behind it, a partner said.

In New York, Lee S. Kreindler of Kreindler and Kreindler on Park Avenue, tried his first aviation case with his father in 1952. Since then, Kreindler says of the disaster cases, "You name them, we were in them."

On the west coast, Kreindler works closely with Morgan in Los Angeles. In San Francisco, Gerald C. Sterns of Sterns Bostwick and Tehin has firmly planted himself among the leading air disaster lawyers.

Once all the claims are filed in the Chicago crash, estimates are that it will take three to four years for them to be resolved - the standard wait in massive disaster cases.

At a 1978 meeting of the Association of Trial Lawyers of American, John V. Brennan, president of United States Aviation Insurance Group that covered the ill-fated American Airlines DC10, provided a glimpse at the legal fees gained as a result of the 1974 crash of a Turkish Airlines DC10 near Paris.

Lee Kreindler's firm handled the cases for the families of 64 victims, 48 of whom were from Japan. Settlements totaled $13.1 million. Legal fees were $2.3 million. Kreindler says Marshall Morgan got more than $500,000 of the fee. Some money went to local lawyers who referred cases to Kreindler and some paid for Kreindler's weekly trips from New York to Los Angeles and his nine trips to Japan.

Speiser Krause and Madole received $23.8 million in settlements involving families of 144 victims and the firm charged $4.4 million in fees.

When the stakes are that high, the competition to get as many of the cases as possible heats up and the attorneys jockey for a command position when the cases finally get to the courtroom.

"In this business, one of the games lawyers play with each other is how many cases they have," said Gerald Sterns. The more cases, the bigger the fee and the greater opportunity to try to take control of the entire case.

In the early days after the 1977 collision of two jumbo jets on a foggy runway at Tenerife in the Canary Islands, Sterns said, the lawyers' boasts about the number of leads they had on lawsuits began to add up to more people than passengers on the two airplanes.

The air disaster specialists often get their cases from family lawyers, who are called in to settle the estate of a victim. As the case lumbers along toward settlement, the family lawyer maintains the local connection, while the specialist assumes the grueling task of assembling the accident case. When the damage settlement is reached, the local lawyer gets a piece of the legal fee, either as a flat referral fee or as specified in a cocounsel" agreement with a specialist.

Morgan knew some people who were touched by the Chicago crash. His dentist shipped some x-rays to Chicago to help identify a victim and later told the widower that Morgan takes disaster cases. A boyhood friend of one of Morgan's partners was killed in that crash and so was a prominent real estate man who knew the owner of the building where Morgan practices law.

Kreindler got a call less than 24 hours after the accident from a man whose brother - a California rock music promoter - was killed in the crash. Seventeen years ago, Kreindler Represented the same man when his parents were killed in another American Airlines crash.

The flamboyant F. Lee Bailey and Aaron Broder, of Bailey and Broder at the Empire State Building in New York, advertise regularly in The New York Times that they take air disaster cases. Broder filed a $1 billion lawsuit last week for one of the Chicago victims.

While newspaper advertisements may be acceptable, ambulance chasing, high-class or not, is not. According to one account, after the collision of the two 747s at Tenerife, a lawyer who once was an airline pilot wrote a letter to family members of the crew offering his services. And there are occasional charges that lawyers have popped up - uninvited - at air crash scenes from Bombay to Norway.

Mass disaster cases may well be highly profitable for the air disaster lawyers, but the litigation is extraordinarily complex and expensive. The sheer volume of work, the demand for aviation expertise and the cost of bringing the case to court usually prompts the family lawyer to turn to the big air disaster firms for help.

"Airplane litigation is complicated - if it's done right," said Donald Madole, ". . . you just can't walk in and say my client bought a ticket, the plane crashed and therefore you owe him money.

"It's not a system of rewards. It's a system of compensation and there's a precise way to formulate that loss," he said.

Xeroxing costs alone in one case can run up to $100,000. Hotel suites have to be rented near the crash site so that the lawyers can have a place to take depositions. The transcripts of those statements can cost another $100,000. Shipping lawyers and documents around the world adds to the cost.

Most of the financing for all this is put up at the start of the case by a committee of lawyers named by the court to act in behalf of all the victims who have filed lawsuits. And the committee always includes lawyers from the air crash disaster firms - established, respected and financially solid.

"You've got to be able to lay it on the line with cash," said Marshall Morgan.

For those who are wondering what ever happened to their application to waive into the D.C. Bar: Anthony Nigro, secretary of the Court of Appeals committee on admissions, says 2,500 to 3,000 of close to 8,000 applications still are being processed. Most of the ones left were filed in March 1978 when there was a crush of lawyers trying to waive in before April 1, when the court changed its admission rules. In Chicago, at the National Conference of Bar Examiners - which does the background checks on applicants, director William H. Morris says that "with luck" his overloaded office could move an application out in 60 days. Nigro says it takes more like eight to 12 weeks, part of which is due to delays in receipt of letters of recommendation for the applicants.

Morris says his employes are hassled by telephone calls from anxious applicants, some of whom pleaded that they were on food stamps and needed quick admission so they could work. Another applicant said his firm's stationery was about to be printed and his name wouldn't be included on the letterhead unless he got into the bar.

Obiter: The U.S. Supreme Court has decided not to take a look at the case of four Philadelphia lawyers who set up a new law firm and then tried to lure clients away from their former employer, Adler Barish Daniels Levin and Creskoff. The Supreme Court of Pennsylvania had upheld a lower court order that said the four would have to find their own business and barred them from any further contact with Adler Barish clients . . . Victor W. Caputy, chief of the training division of the U. S. attorney's office here, has received the Justice Tom C. Clark award from the D.C. Chapter of the Federal Bar Association. Caputy, who was sworn in as an assistant U. S. Attorney in 1951, coaches fledgling - and not so fledgling - prosecutors on trial techniques . . . Also in the U.S. courthouse, Brian W. Shaughnessy, chief of the fraud division, which handled the GSA scandal investigations, has left for private practice with Cohan, Schaumber and Shaughnessy . . . A committee of the American Bar Association will hear testimony today and Tuesday at the Mayflower Hotel on intimidation of crime victims and witnesses. CAPTION: Picture 1, Firemen walk past one of the engines of American DC-10 in Chicago crash. UPI; Picture 2, Landing gear is one of the largest pieces remaining after air crash in Chicago that claimed 274 victims. UPI