By demanding the right to establish free trade unions, striking workers in Poland have laid a mine field not only for Edward Gierek's government but for the entire Soviet Bloc.

The issue is at the core of the current crisis in Poland and Western analysts here believe it cannot be resolved short of radical political changes.

The strikers, according to East European sources, are in effect making demands for a pluralistic society in which the unions would become an established source of power outside Communist Party controls.

If accepted by Gierek, it would amount to the creation of a second party representing workers' interests and undermining the legitimacy of communist authorities. According to these sources, even nonaligned Yugoslavia -- which has evolved a self-management system that gives workers considerable say in the running of their factories -- has not permitted independent trade unions.

Gierek's initial pledge to permit free and secret trade union elections contrasts with Lenin's concept of unions as "schools of communism" under party supervision. Like other organizations and public bodies, the trade unions in all communist countries are instruments of the party's authority.

Ideologically, since the Communists present themselves as the vanguard of the working classes, the aims of the party and the unions must be seen as identical. That system eliminates the possibility of conflicts in interest.

On the practical level, communism has abolished private property and the mechanism of the competitive market. It has replaced them by government guidelines on virtually all aspects of economic life, ranging from wages and prices to production levels, taxes and allocation of resources.

Thus independent trade unions could be in frequent confrontations with the government not only in bargaining over wages but also over the entire range of economic and social policies. This, according to East European officials is not acceptable.

Moscow today made clear the unacceptability of such evolution in Poland by limiting mention of Gierek's pledge to permit free and secret trade union elections.

The government news agency Tass distributed a dispatch last night in its Russian service that quoted Gierek's promises ot the workers. But the Soviet media today, while giving a substantive account of "political and economic" difficulties in Poland, eliminated Gierek's statement on the trade union issue. Instead, the Communist Party newspaper Pravda said "the forthcoming Polish trade union congress should decide about the place and role of the trade unions."