Justice William H. Rehnquist yesterday became the sixth Supreme Court justice in the last two months to warn of a deterioration in the quality of judging in America because of escalating caseloads and a bureaucratized federal judiciary.

In a speech prepared for delivery last night at the University of Kentucky, Rehnquist said that judges no longer have adequate time to devote to their cases and are in danger of becoming "managers," delegating the real power to subordinates. Efforts to improve the situation by creating more judgeships may only result in less qualified people sitting on the bench, Rehnquist suggested.

Rehnquist thus joined what has become an unprecedented, though apparently uncoordinated, series of critiques of the judiciary offered by ordinarily reticent members of the court. The six justices have offered different analyses and solutions but with a common theme: the federal judiciary and the Supreme Court are overloaded and stretched too thin.

Justice John Paul Stevens, the first to speak out, said at the American Bar Association meeting in San Francisco last month that the court's entire workload, from the selection of cases to the writing of opinions, may be suffering as a result of overload.

Justice Byron R. White said that for the first time in his 20 years on the court, the justices could not complete their work last term and are already almost fully booked for the term that starts in October. Justice Thurgood Marshall complained that the justices are making too many hasty summary decisions, displaying a "cavalier" attitude towards the rights of those affected by some decisions.

Justice Lewis F. Powell Jr., striking a theme similar to Rehnquist's, said the lower courts now "resemble business operations" and are becoming "bureaucratized." If it is overdone, he cautioned, "the rule of law -- reduced to wholesale justice by the crush of cases -- could be the ultimate victim."

"There is a limit to human endurance," Justice William J. Brennan Jr. said in his recent speech about the court's workload.

New statistics released this week by the Administrative Office of the U.S. Courts underscored the problem. Between 1975 and 1982, the number of civil cases filed in the federal courts rose from 117,320 per year to 206,193. In response, the number of judgeships in the district courts and the courts of appeal was increased from 497 to 647. According to the statistics, however, that was not enough. The caseload per judge increased by 36.5 percent.

The Supreme Court, at the pinnacle of the system, felt the brunt. The number of justices stayed the same during those same years. But the number of filings rose from about 3,900 to nearly 4,500 last term, a record.

Other branches of government have solved similar problems by massive expansions in the number of assistants and aides. The judiciary has done some of that. It now employs 14,500 people. But its ideal, the image of a Justice Oliver Wendell Holmes Jr. retiring to his study to contemplate each case, does not mesh with the idea of squadrons of law clerks and administrators and the computer terminals on which Supreme Court opinions are now processed.

"I suspect," Rehnquist said in his speech, "that it may not be too long a leap" from the current situation to "opinion writing bureaus which many federal agencies rely upon. The commissioners of the agency in question decide an issue before them, and summon one or more members of the opinion writing bureau to write an opinion justifying the result which they have reached."

He said that unlike the executive branch chores, "no substantial part of the judicial function can properly be delegated by the person who holds the commission." When it is parcelled out, he said, "it exacts a price."

In addition, he said there is the possibility "down the road that indefinite multiplication of judicial positions may well detract from the prestige of the job, an important element which has enabled the federal judiciary to command the respect which it has today."

"To the extent that the element of prestige is gradually phased out of any judgeship, whether federal or state, we run the risk of depleting even further the reservoir of available talent" to fill judgeships, Rehnquist said.

It is understandable that the justices are speaking out at this time of year. Currently, they are combing through more than a thousand cases from which, at a conference on Sept. 27, they will select 30 or 40 for full review. Generally, they use memos three to eight pages long prepared by clerks on each case. In a single term, the total reading for each justice can average 20,000 pages before they even get to the more publicized work of the court, deciding and writing opinions.

The public never hears about 95 percent of the filings, called petitions for certiorari or jurisdictional statements, that come to the Supreme Court. For that it should be grateful. Most of them are technical with legal questions that sound something like this: "Does federal law preclude requiring a fiduciary to collect and pay a sales or use tax based on a liquidation sale under jurisdiction of federal bankruptcy act?" (California State Board of Equalization vs. Western Marina Corp.)

The root of the problem is the "litigation explosion," and the tendency to go to court to resolve every dispute. In addition, prison inmates petitioning the court repeatedly for their freedom cause some of the crush.

But many observers say lawyers, who should know better, bring too many cases to the high court. Privately, some justices and clerks refer to much of this outpouring as "trash," which doesn't stand a chance of being accepted for review. White, in his speech, estimated that about 60 percent of the filings "have no merit at all" and that only about 20 percent deserve "serious attention."

"The vast majority of the filings are from lawyers who have never been there," said A.E. (Dick) Howard, University of Virginia law professor and court expert. "They have no intuitive sense of what's worthy and no one to tell them.

"So they go to the big court. . . . There's also an ego factor. A lawyer wants a moment of glory. And there are breast-beating promises to clients: 'I'll take your case all the way,' and that sort of thing," Howard said.

"The discipline would have to come from the bar," said Harvard Law Professor Paul Freund, who headed a commission that studied the court's caseload in 1970.

"And it seems like baying at the moon to keep reminding lawyers of this. They do have a duty to their clients," he said. "And in this age of burgeoning malpractice suits, one can understand why they exhaust all avenues."

Most court watchers are critical of the justices themselves for not exercising discipline in selecting cases and thus overbooking themselves. In the upcoming term, any cases accepted after November will not be heard until the following term, an unprecedented delay.

To help reduce the Supreme Court's workload, Congress is considering elimination of a technical category of cases, called the "mandatory docket," to which the justices must devote unusual attention. More far-reaching ideas, such as the creation of a new court to help select the caseload for the justices and Stevens' proposal to give such a new court total control over the docket selection, are considered too controversial to pass Congress.

Rehnquist said Congress has added to the problem by enacting numerous laws, many little known to the general public, that have created new areas of litigation in the federal judiciary, such as a 1975 Federal Child Support Enforcement Act and the 1972 Motor Vehicle Information Cost Savings Act.

And Chief Justice Warren E. Burger, in a major speech to the American Bar Association last winter, called for a renewed effort to channel disputes out of the court system for resolution.