Chief Justice Warren E. Burger, calling the country's prisons a "disaster," yesterday proposed a national training center for prison guards and mandatory training for inmates in order to fight crime and improve prison conditions.

Burger, speaking at commencement ceremonies at the George Washington University law school, warned the more than 400 graduates that "the consequences of the present system will fall on you and your children for a long time" unless something is done to improve prisons.

Burger, who received a standing ovation when he was introduced, has spoken often of the need for corrections reform, but yesterday he went into more detail than he has before, proposing two programs which he called "small steps" but "affordable" even in terms of the "political and economic realities of 1981.

"To do all the things that might have some chance of changing persons convicted of serious crimes will cost a great deal of money," Burger said, adding that "1981 is hardly the year in which to propose large public expenditures" for new prisons and major programs. "Small steps are better than none," he said.

Citing the crime committed by prisoners after they are released and the turmoil inprisons in the last decade -- including three riots last week in Michigan and Nevada -- Burger compared the situation to the automobile production lines in Detroit.

"Recidivism is the penologist's word for 'product recall,'" he said. "Our current rate of recall [the number of repeat offenders] is a disaster."

Burger praised the FBI's national police academy for its training of thousands of state and local police officers, saying that training has "vastly improved" the quality of police in terms of efficiency and the "kind of law enforcement a decent society should achieve."

Burger called on President Reagan and Congress to "proceed at once" to establish a national academy of corrections to provide training for prison personnel. Although he gave no figures, Burger estimated that the cost of such an institution wuld not be "great," particularly if, for example, the facilities at the FBI academy in Quantico could be shared by the corrections academy.

His second proposal, which he suggested could be phased in over a longer period of time, is that all inmates who cannot read, write, spell or do simple arithmetic be forced to learn to do so.

"The number of young, functional illiterates in our institutions is appalling," Burger said. "Without these basic skills, what chance does any person have of securing a gainful occupation when that person is released and begins the search for employment -- with the built-in handicap of a criminal conviction?"

Burger, criticized by civil libertarians for a speech last February when he attacked the legal system for being too lenient on criminals, said he anticipated that perhaps some might consider the "mandatory aspect as harsh."

His suggestion, which drew laughter from the audience, was that the total work and study hours for the inmates, "be no greater than we demand of the 15,00 young Americans who are cadets in our service academies of the many more thousands of law students."

Burger also proposed a large expansion of vocational training for inmates so that "a prisoner would not leave the institution without some qualifications for employment in the construction, manufacturing or service industries."

An inmate who refuses to participate in these mandatory training programs could be induced to do so by incentives "including shortening the sentence," he suggested.

Burger emphasized that he believes society has only a "moral obligation" not a legal or constitutional one, to improve prison conditions and help inmates improve their lives.

"The Constitution properly mandates due process," Burger said, "but it mandates nothing concerning the subject of punishments, except that they be not "cruel and unusual.' "