Siberia's frozen riches are slow to thaw for the Soviet economy

''Go east, young man, and grow up with Siberia. . . .''

That, at least, is the idea.

Yet the Soviet Union's search for a ''Siberian solution'' to its economic slowdown of recent years has run into problems.

There has been at least one clear success story: a huge spurt in Siberian oil and, more recently, natural gas. (Oil output in 1980 was some 10 times the figure for a decade earlier. Production of Siberian gas, seen as key to the overall Soviet energy picture in the 1980s, expanded by a factor of about 20 from 1970 to 1980.)

This is particularly important at a time when Moscow is importing record amounts of grain, since energy exports are the Soviets' single largest source of hard-currency earnings.

Construction also continues, although it is behind schedule, on a new Siberian rail line designed eventually to tap an array of other regional riches for domestic and export purposes. There is timber, coal, aluminum, gold, iron ore, bauxite, copper. The list goes on. The railroad is now slated for completion in October 1984.

One Western businessman, asked about a year ago to assess overall Soviet economic prospects, simply unfurled a resource map of Siberia and said: ''The bottom line is that the region is fabulously rich, even if you consider only the area near the new rail line.''

This and most other foreign analysts here argue that - sooner or later, in one way or another - Soviet planners will turn Siberian wealth to enormous advantage.

Yet the pace and range of Siberian development will be crucial to overall economic fortunes. The great majority of the Soviet Union's roughly 270 million people lives in the European part of the country. The great majority of the nation's energy, timber, nonferrous metal, and various other resources lies in Siberia and the Soviet Far East. But efforts to intensify development of Siberia have met a number of snags.

One problem is people. Officials up to and including President Leonid Brezhnev have, like Horace Greeley's advice in reverse, stressed the importance of luring large numbers of new settlers eastward to Siberia. Drawn sometimes by high pay, sometimes by adventure or a sense of patriotism, tens of thousands have obliged. But most come to work, far fewer to settle.

There are shortages of housing, recreational and child-care facilities, consumer goods and food. A recent survey by a Soviet journal of workers on the new railroad elicited complaints on these scores, and found only 13 percent of respondents wanted to settle in Siberia.

On the production side, Siberian projects must cope both with natural difficulties and with overall Soviet economic inefficiencies. Reports in the official news media speak of delayed deliveries of needed materials, and of lack of coordination in the planning of various government ministries involved in Siberian projects.

One particular ministry, in charge of the coal industry, has been reprimanded for neglecting prospects for strip-mining in Siberia at a time when production in the traditional European coal area has been on the decline.

(Recent figures, showing the first sustained increase in overall Soviet coal output for several years, suggest the criticism may have been taken to heart. But a coal ministry official queried by The Christian Science Monitor said problems remain and that it would be premature to speak of a ''turnaround.'')

Original hopes for Western and Japanese participation in Siberian development , meanwhile, have yet to pan out fully. Various major projects are under way. Japan, the Soviets' natural geographic partner in Siberia, is involved in timber and coal projects there, while also participating in an offshore oil project in the Far East. Western Europe, for its part, is helping with a huge Siberian gas- export line that US President Reagan would have liked to stop.

Yet other ''resource-for-technology'' deals with Japan and the West have not materialized on the scale once hoped for. This applies especially to the Japanese, and the Soviet prime minister said as much in a recent interview with a Japanese newspaper. Various Soviet-American schemes - like a 1972 proposal to ship Siberian gas to the US - have expired on the drawing boards.

Strained Soviet political relations with Tokyo and Washington have been one deterrent to enlargement of joint efforts to develop Siberian resources. A softening world market for various of these resources is surely another factor.

The Soviets, meanwhile, have come increasingly to focus on the idea of shifting domestic resources into Siberian development. One central feature of this strategy - still, of course, likely to involve the import of relevant technology and equipment - would be to site energy-intensive industrial ''complexes'' close to Siberian energy sources. Similarly, a senior official explained in an interview, efforts would be made to ''extract and process (Siberian) raw materials on the spot.''

This promises to be an expensive business, in the short run, and thus could well spark resistance from competing national interests.

A prominent advocate of intensified Siberian development, economist A. G. Aganbegyan, suggested as much in an article last year. He wrote that ''quite often, planning bodies, researchers working in the sphere of economics, and ministries'' raise objections to focusing on Siberian investment. Among them, he said, was the contention that ''the development of Siberia's natural resources is more expensive (than investing elsewhere), and the returns are not immediate.''