Last summer, as millions of people watched the Live Aid rock concert on television screens around the world, the audience here was restricted to a small group of people given passes to the main state television studio.

Now that select number is growing as videocassettes of the hugely popular concert make the rounds in Moscow, beaming Mick Jagger, Tina Turner and other forbidden western acts into Soviet living rooms.

The Live Aid tapes are an example of the dilemma faced by the Soviet government as the video mania spreads here. What is denied by the government -- for whatever reason -- can increasingly be provided by videocassettes the size and weight of a paperback book, dubbed, traded, rented, bought and sold through various back-door networks.

The spread of videocassettes is no longer restricted to Moscow and its elite circles of diplomats, artists, athletes and others allowed to travel abroad. In the central Russian city of Voronezh where Soviet videocassette recorders are produced, the local electronics store sells about 150 a month, and the local videocassette lending library has a regular clientele of about 200 and an inventory of 1,000 cassettes.

In the last year, videos have become accepted in the Soviet Union, which has a promising home entertainment market. Most socializing here goes on in private apartments and there is a growing recognition that videocassettes can be a useful educational tool, as one proponent said in an article recently, for everything including "how to run a household, how to renovate your apartment, how to train your dog . . . how to drive, how to swim."

Following Voronezh's example, at least 12 videocassette libraries opened in the country last year. There are plans to increase production of cassettes and of the video machines themselves. One newspaper has begun a video column and the All-Union Film Library Association has created a department for printing and distributing videos.

"We cannot wait passively until our 'video market' is completely captured by an uncontrolled influx of foreign videotapes," said Yevgeny Voitovich, head of film distribution for the Committee on Cinematography.

But Soviet attempts to compete with the lure of western videocassettes are handicapped from the start, since part of the attraction for the Soviet viewer is precisely the escape from regular Soviet fare.

"It is a keyhole into another world," said a young Russian who is in the market to buy a videocassette recorder.

Even the newspapers admit that the Soviet offerings at the video clubs are too limited -- heavy on both classics and cartoons -- and in many cases too boring. So far, for instance, there is nothing to compete with the West's music videos, which are now taped by Soviet citizens traveling abroad and put on the circuit here as the latest and hottest format for underground rock and roll.

As an employe in one store explained, the shortage of Soviet cassettes is not due to demand for what is recorded on them but for the tapes themselves. Blank tapes are very expensive here, costing upwards of $50, and often in short supply. The price of cassettes with Soviet films is not much more, and they can be erased and taped over with foreign films.

Articles have appeared about improving the range and quality of Soviet video fare. In Voronezh, the director of the club said the Moscow distributor has promised that some foreign films will be made available this year.

Foreign films are scarce here both for ideological reasons and because of Soviet reluctance to pay high prices for the copyright on first-run films.

Despite the promotion in the press, many consumers here sense an official reluctance to embrace the video revolution wholeheartedly, precisely because it can never be wholly controlled.

There is a lingering uneasiness about the whole business, built up by campaigns against imported films described here as dealing in pornography, violence, mysticism and "blatant or camouflaged anti-Sovietism."

As in other areas of the economy, Soviet acceptance of the video is best judged not by words but by five-year plans. Production goals by the year 2000 call for an increase of 120,000 videocassette recorders, 60,000 of them by 1990. But given the demand that exists -- 2,000 are on the waiting list to buy a machine in Moscow and 1,600 in Voronezh -- the numbers are strikingly low.

Prices, meanwhile, are still staggeringly high. A foreign-made videocassette recorder system can cost 3,000 rubles, about $4,000, almost as much as a second-hand car. A Soviet video recording system, the Elektronika VM, costs 1,235 rubles.