The Supreme Court yesterday struck down tight restrictions on advertising by lawyers, freeing all the professions for promotional campaigns more comparable to ordinary business advertising.

The justices unanimously declared unconstitutional Missouri's advertising rules, which are similar in many respects to those in more than 38 states. The Missouri restrictions banned mass mail advertising, and dictated the exact words lawyers could use to describe their qualifications in ads.

The rules were challenged by a lawyer disciplined under those rules for, among other things, advertising himself as a "personal injury" lawyer instead of a "tort" lawyer and for advertising his membership in the U.S. Supreme Court Bar.

No one challenged the truthfulness of the claims, Justice Lewis Powell wrote for the court, and restrictions are appropriate only when primarily intended to prevent deception or false advertising.

The ruling, which affects doctors, engineers, architects and others as well as lawyers, is the court's most important elaboration on lawyer advertising since its 1977 decision lifting what had been an absolute prohibition.

Since then, ads for lawyers have become commonplace in newspapers and yellow pages. But, with some exceptions, they have been brief and staid. They have also been carefully scrutinized by bar disciplinary committees for their "dignity" as well as their truthfulness.

Yesterday's decision is expected to encourage more experimentation in such advertising.

The lawyer involved in yesterday's case was identified only by initials: R.M.J. The lawyer, a former Securities and Exchange Commission attorney, took out ads in newspapers and yellow pages and sent out a mailing after he moved to St. Louis in 1977.

In the process, he broke several Missouri rules. The Missouri rules required lawyers to confine descriptions of their specialties to pre-determined categories. The rules said a lawyer could call himself, for example, a practitioner of "family law" or "property law." This lawyer, instead, used the terms "divorce-separation" and "real estate" in his ads.

The rules prohibited a listing of the courts where a lawyer was licensed to practice. The Missouri lawyer, living near the Illinois-Missouri border, advertised himself as licensed to practice in Missouri and Illinois and, in bold letters, stated that he was admitted to practice before the United States Supreme Court.

In addition, the lawyer was charged with mailing announcements of his practice to persons "other than lawyers, clients, former clients, personal friends and relatives" in violation of Missouri rules.

The Missouri State Supreme Court upheld a reprimand for these violations. Powell's ruling yesterday reversed that action.

Powell said that misleading or false advertising may be "prohibited entirely," and states have some authority to impose other kinds of restrictions. They may, for example, require advance screening of any mailings.

But they must provide a "substantial" reason and any controls should suit those reasons in the least restrictive manner, he said.

In the Missouri case, he said, "there is no finding that the lawyer's speech was misleading, or that restrictions short of an absolute prohibition would not have sufficed to cure any possible deception.

". . . Although the states may regulate commercial speech, the First and Fourteenth Amendments require that they do so with care and in a manner no more extensive than reasonably necessary."

District of Columbia, Maryland and Virginia lawyers were still studying yesterday's ruling, but many said they did not expect a direct immediate impact in their jurisdictions because their regulations are not as specific as Missouri's.

Authorities on lawyer advertising, however, suggested that the ruling's impact could go beyond the decision itself by softening the stiff scrutiny now applied to advertising.

"That has deterred a lot of people from running ads at all," said Lori Andrews of the American Bar Foundation in Chicago.

In other action yesterday:

* The court, in a ruling further limiting the powers of federal judges to interfere with state court criminal proceedings, voted, 6 to 3, to reinstate the conviction of a former New York policeman charged with murdering a pimp and a prostitute.

The jury's verdict had been reversed in the federal courts because the prosecutors failed to disclose that one juror, during the trial, had applied for a job in their office. The lower courts said the juror might have been prompted to convict the defendant in order to get the job and the prosecutors should have disclosed the application during the trial.

The lower federal courts ordered a new trial for the ex-policeman, William R. Phillips, who was a witness during the 1971 Knapp Commission probe of police corruption in New York.

Justice William R. Rehnquist, writing for the majority in Smith Vs. Phillips, said that juror prejudice must be "actual," not simply assumed or "imputed" as it was in this case. In addition, he said the lower courts went beyond their authority in second-guessing the state courts, which had upheld the conviction.

Justice Sandra Day O'Connor joined the opinion but wrote separately to say that it does not foreclose the use of "implied bias in appropriate circumstances."

Justices Thurgood Marshall, joined by Justices William J. Brennan and John Paul Stevens, dissented. They said that even the appearance of prejudice can taint the impartialty of a jury.

* The court also significantly increased Indian authority over their federal reservations, upholding the right of tribes to impose taxes on the natural resources extracted from their reservations by oil companies.

The taxes, which provide millions of dollars to tribes all over the West and Southwest, were challenged by the companies, which already pay money for drilling leases, on the ground that they exceeded tribal sovereignty over their territory.

By a 6-to-3 vote, the court said the tribes were within their powers under both the Commerce Clause of the Constitution and congressional actions over the years.

Justice Thurgood Marshall wrote the opinion. Justice John Paul Stevens, joined by Chief Justice Warren E. Burger and Justice William H. Rehnquist, dissented in Merrion Vs. Jicarilla Apache Tribe.