The U.S. military is so short of doctors that there might not be enough of them to give adequate care to the wounded if war should break out, Army Secretary Clifford L. Alexander Jr. said yesterday.

Terming military health care a "very grave" problem, Alexander said it would be "tragic" if the armed services fail to prepare medically for "a high casualty rate in this era of sophisticated weaponry."

Alexander's grim report to the annual meeting of the Association of Military Surgeonos is the latest warning of a crisis in military health care, both for people on active duty and their dependents.

The basic problem is that there are not enough military doctors to go around. At the same time, there is widespread disillusionment among those physicians already in the service, leading to resignations which make the present shortage even more severe. There is no draft law to enable the services to make up shortages.

"The most disturbing aspect of the problem from my perspective," Alexander said yesterday, "is that the current status means we may not be able to ensure adequate medical support of a major conflict in Europe.

"We can anticipate a high casualty rate in this era of sophisticated weaponry," Alexander continued. "Even the possibility of exposure to chemical, biological or nuclear measures cannot be entirely ruled out in light of what we know of Soviet war fighting doctrine."

Alexander said that "the crux" of the problem is the shortage of doctors, but recruiting them into the armed services "is not an easy task."

Pentagon health executives complain that the scholarships the military services can offer to future doctors are not as attractive as those available from the Health, Education and Welfare Department. They are pushing to eliminate the differences.

The Army figures it needs 5,856 doctors on active duty but only has 4,140 at the moment, a shortage of 1,716 physicians. The doctor shortage in the reserve unit, Alexander said, is "particularly acute."

The Army secretary said two-thirds of the medical support if war came would come from the serve forces. Given the shortages, Alexander said, "perhaps the time has come to consider some sort of reserve obligation for beneficiaries of all government-funded scholarship programs."

Some government officials have concluded that the only long-term solution to the problem of caring for people on active duty, retired military people and dependents is to contract more medical services out to civilian doctors. Alexander yesterday indicated he felt there was a limit as to how much of this care should be contracted out.

"Providing medical care for the military by the military" is the most cost-effective way to do it," the Army secretary said.