McDonnell Douglas Corp. is a company very much at home in St. Louis. In a heartland city that seems to breed cautious, tightly managed firms, the aerospace giant has blended in well.

But the crash of one of its DC10s in Chicago has begun to shake the normally steady corporation. Signs of management fatigue are evident.

Already sharply at odds with federal officials over safety of its aircraft, McDonnell Douglas openly split yesterday with American Airlines, one of its chief customers. The two companies got into a heated spat over whether proper procedures were followed in the maintenance and care of the DC10.

It was a highly unusual rift in an industry generally known for keeping its temper. In other instance, too, company spokeman have become defensive and uncooperative.

"This is not the kind of thing they need," said Wolfgang Demisch, an analyst with Smith Barney, Harris Upham Co., referring to the public bickering. "McDonnell Douglas is really not handling this very well."

In addition to all the psychic stress, the company will surely suffer financially as a result of the crash, though the full extent of the cost is still unclear.

McDonnell Douglas will be tied up in hundreds of millions of dollars worth of damage lawsuits in connection with the 275 people who died in the crash. A prolonged grounding of the DC10 could cost millions more. If a redesign of the aricraft is ordered, the expenses could become monumental. And nagging doubts about the firm's general ability to build airplanes could spoil future sales prospects.

Despite current dark times for the firm, a number of industry analysts remain unwilling to write McDonnell Douglas off. "We're still very positive about the company," said Don Spindel with A. G. Edwards & Sons Inc. of St. Louis. "Taking the long term, the company is probably financially strong enough to absorb the costs."

The company does have an impressive balance sheet. In the last few years, it has built up cash accounts to something over $600 million and cut debt to less than $75 million.

That the company should be so financially liquid is a credit to the unchallenged and frugal-minded direction of patriarch James S. McDonnell, who built the company from a small design, repair and construction business in 1939 and, at 80, is still active as chairman.

"Old Mac," as he is known, continues to pilot the compaay with the help of his nephew, Sanford N. McDonnell, who succeeded him as chief executive in 1972. The elder McDonnell and two sons, John F. and James 3rd, who are also involved in managing the company, control about 20 percent of the firm.

The Douglas half of the company is a recent addition, acquired only a dozen years ago when McDonnell was looking to diversify out of what was then - and still is - its mainstay operation, the building of military aircraft. The commercial aircraft business seemed a natural choice.

McDonnel bought Douglas cheap. The company had been started by Donald Douglas in 1920 and, while it dominated the commercial aircraft industry for a time, it had come under increasingly stiff competition from Boeing and Lockheed. Its production costs were up and its cash was way down.

Douglas' production facilities are still where they were first built in Long Beach, Calif., and that is where the DC10s are made. The fit between the West Coast and St. Louis has never been close.

"It's called McDonnell Douglas, but there's never really been a complete fusion," said Demisch. "There's still somewhat of a us-versus-them attitude."

McDonnell has yet to make a profit out of Douglas. Military aricraft sales - particularly, the F4 Phantom fighter, the F15 for the Air Force and the F18 for the Navy - continue to carry the corporation. Profits from these sales have effectively financed the expensive development of the DC10, which has been flying eight years. They have also bankrolled McDonnell Douglas' expansion into computer services and electronics.

Commercial aircraft accounted for less than a quarter of the company's $4.3 billion in sales last year, and registered a loss of $60.3 million, about $10 million more than in 1977.

McDonnell had been looking forward to turning a profit soon on the wide-bodied DC10s. The magic sales number was 400, which company officials expected to reach by 1981. They had gambled on the plane, deciding last year not to follow Boeing and the European aviation consortium, Airbus Industrie, who were designing newer wide-bodied models for the 1980s.

The gamble still might pay off. No airline has yet canceled standing DC10 orders. And Varig Brazilian airways placed an order for five of the big jets. Moreover, even if an airline wanted to replace its DC10s, it probably could not because of the huge amounts of money invested in the planes and the expense to duplicate training and maintenance facilities for another type of aircraft. CAPTION: Picture, Workers at McDonnell Douglas in Long Beach, Calif., continued to turn out DC-10 airliners yesterday. AP