Lawyers for John W. Hinckley Jr., officially admitting that there is no dispute that Hinckley shot President Reagan and three others March 30, said yesterday that they will argue that Hinckley was insane at the time of the incident and should not be held criminally responsible for his acts.

Hinckley faces up to life in prison if convicted of charges in a 13-count indictment. But if he is found not guilty of those offenses by reason of insanity, D.C. law requires that he immediately be committed to St. Elizabeths Hospital, the federal institution in Southeast Washington for the mentally ill.

Hinckley could be released from there within 50 days, if the court determines, based on psychiatric evidence, that he is no longer a danger to himself and to others because of mental illness.

The lawyers also asked yesterday for separate trials and separate juries on the questions of Hinckley's actions and on his mental state if the government does not agree to the facts of the shooting as outlined by Hinckley's lawyers.

The defense lawyers also asked the court to prohibit the government from using as evidence statements that Hinckley made to law enforcement officials and psychiatrists after his arrest, and reserved the right to request that trial proceedings be moved outside Washington.

Yesterday's court filings made it apparent that the trial of Hinckley will focus on his mental state at the time of the shooting and probably will be marked by long and detailed testimony from psychiatrists and psychologists on both sides.

No trial date has been set, but it is not expected to begin for several months.

Hinckley's lawyers filed papers yesterday in U.S. District Court asking federal prosecutors to agree to a formal stipulation that their client fired the shots from a .22-caliber revolver that wounded Reagan, presidential press secretary James S. Brady, U.S. Secret Service agent Timothy J. McCarthy and D.C. police officer Thomas K. Delahanty outside the Washington Hilton hotel.

Such an agreement would eliminate the need for a trial on the basic elements of the case, and leave only the question of Hinckley's mental state at the time of the shootings.

Government prosecutors rarely join in such a statement of facts in a case in which an insanity defense is raised, however, because they contend that facts surrounding an incident can have a direct bearing on the question of the defendant's mental state.

If that happens in this instance, Hinckley's lawyers asserted yesterday, two juries should be empaneled for two different trials.

Courts customarily allow a two-stage trial in such cases. The first stage involves whether the defendant actually committed the crime he is charged with. If convicted, the defendant would then argue in the second stage that he should not be held responsible for the crime because he was insane at the time it was committed.

The routine practice in the District of Columbia is for a single jury to hear both stages of such insanity cases. Courts have determined that the jury that determines the defendant's mental state at the time of a crime should have the benefit of hearing the facts underlying that offense.

But Hinckley's lawyers argued in court papers yesterday that the emotional impact of the prosecution's evidence in the first stage of the case will be so great that a single jury would then be unable to consider objectively the psychiatric testimony that would be presented in the second trial.

"Inevitably, there will be the kind of patriotic wrath that any American must feel when the President of the United States is subjected to such a violent attack . . . .

"And, predictably, there will be a desire to make an example of John Hinckley in an effort to deter others from following in his footsteps. Simply put, this evidence will inflame the jury's passions," the defense lawyers said.

In asking the court to disallow statements that Hinckley made to law enforcement officials immediately after his arrest, the defense lawyers acknowledged that he had waived his right to remain silent. But he repeatedly asked to talk with an attorney and was questioned without one present, and that was improper, they said.

The defense lawyers also contended that statements Hinckley made during a psychiatric examination held shortly after his arrest should not be admitted.

The defense said those statements should be excluded because Hinckley already had admitted he was competent to stand trial and objected to the examination to determine mental competency, during which the statements were made.

Hinckley's defense lawyers also want the court to exclude from evidence all statements that Hinckley made to a team of doctors during four months of examinations at the federal correctional institution at Butner, N.C.

The lawyers contend that the court did not have the authority to order Hinckley to submit to those tests over his lawyers' objections. Moreover, the lawyers contend, Hinckley's constitutional rights were violated because he did not have a lawyer present during interviews at Butner. Hinckley is currently in custody at the army stockade at Fort Meade, Md.

The issue of the insanity defense -- which the courts have long found a troublesome mixture of law and psychiatry -- is expected to raise novel and complicated questions about whether to hold Hinckley criminally responsible for his acts.

In anticipation of a trial on an insanity defense, Hinckley has been undergoing extensive examinations by psychiatrists and psychologists retained by both the prosecution and defense.

To reach a decision of not guilty by reason of insanity, the jury would have to find that Hinckley, at the time of the crimes, suffered from a mental disease or defect that left him unable to conform his conduct to the law or to appreciate the wrongfulness of his acts.

The jury would be instructed by the court that a mental disease or defect means any abnormal condition of his mind that affected his mental and emotional processes and substantially impaired his capacity to control his acts.

In their court filing yesterday, Hinckley's defense lawyers also left open the possibility that they might make an argument just short of insanity -- that Hinckley's mental state was so diminished at the time of the offense that he could not have had the specific intent to commit the crimes he is accused of.

The government is scheduled to respond to the defense filings by Oct. 16. A hearing on the issues is scheduled for Oct. 30 before Judge Barrington D. Parker, who will preside at Hinckley's trial.