The Soviet Union, anxious to make the leap into the age of high-technology, started the school year Monday with a new program introducing the computer to students in the upper grades.

The urgency of the school computer program stems from the Soviet Union's anxiety about being left behind by the West's technological competition. Soviet schools are several years behind U.S. schools in introducing computer courses.

The secondary school computer program was one of the first initiatives announced after new Soviet leader Mikhail Gorbachev came to power last spring and is the keynote of his repeated emphasis on the need to speed up Soviet technological progress.

A leading Soviet computer expert, in an article last April, called the introduction of a school course on computers a matter of "state necessity" and a "prerequisite" for improving the nation's economic efficiency.

Computer training in the schools had been discussed before, but the announced directive from the ruling Politburo last March turned it into a crash program.

Provisional textbooks are being printed, and a competition for a permanent textbook is set for 1986. About 70,000 secondary school teachers were given training courses this summer and the production of Soviet-made computers -- the Agat and DVK -- has been stepped up by "the thousands," according to one newspaper report.

One published account said that under the program, ninth graders will receive 34 hours of instruction on computers and 10th graders, seniors in the Soviet system, will receive 68 hours.

But as other articles in the press have candidly pointed out, not all schools or teachers are ready for the new program this year. In Minsk, for instance, one paper predicted not long ago that there would be only one computer for every five schools by 1990.

The newspaper Trud admitted last week that there would be two different kinds of computer courses when the schools opened Monday -- "one with machines and one without them." In the latter situation, the article said, students will have access to computers at city centers.

Andrei Ershov, an academician and leading advocate of computer training in the schools, pointed out last spring that the cost of the new program would be "colossal," requiring more than 1 million personal computers in secondary schools.

While awaiting an adequate supply, schools must make do with films and books about computers and their uses, building a groundwork of "theoretical knowledge" while getting ready for the practical uses, he said.

The Soviets intend not only to produce more computers and create a network to service and repair them but also to accustom workers in all spheres to using the machines.

In a society where many cashiers persist in using the ancient abacus to tote up sales, the psychological adjustment to the computer age is expected to be difficult.

The crash school program is a key step in that direction. "Computer technology is making inroads into all spheres of human activity and so we must be taught from the school bench how to use computers," a Moscow newspaper said in an article on the Politburo directive last March.

[In the United States, computer training entered the secondary school curriculum by 1981, said Henry J. Becker, a research scientist at The Johns Hopkins University's Center for Social Organization of Schools in Baltimore. When he surveyed computer use in U.S. schools in 1983, Becker said, the typical high school had four computers for a student body of 700 and "a small number of students -- about 10 or 11 percent -- got to use the computers for about 45 minutes a week." In a resurvey this year, Becker said, he found three times as many students and teachers using computers but concluded that any extensive training "is still a minority experience."]

A slight defensive tone has crept into the many articles about computers that have appeared here lately. Readers are told that Moscow's School No. 444 was a pioneer in computer training during the 1950s and that western countries are not that much further along.

But there are also frank admissions that in this realm, Soviet schools could benefit from the experience of other countries -- and possibly from the purchase of western computers to put in the schools.

The shortage of computers and trained teachers has been compounded by what education specialists here describe as the natural conservatism of the classroom teacher.

In an article in the government newspaper Izvestia on Thursday, Deputy Education Minister Fedor Panachin insisted that experiments with computer education had enhanced students' ability and eagerness to learn all subjects.

"We consider . . . that there is no reason for any concern about a slight reduction in time spent on other subjects," said Panachin, who made it clear that school authorities envisage one day using computers in all subjects, not just limiting them to special classes.

In the schools as in the rest of society, the official Soviet view of computers, while extolling their uses and necessity, also strikes a note of caution.

Ershov, for instance, wrote that computers should be used "to strengthen positive character traits" in schoolchildren and not to develop "a sense of individualism and isolation from their comrades."