In a run that is feared may soon turn into a rush, an increasing number of Polish people are asking for refuge in the West.

Figures provided recently by the Interantional Committee on Migration in Geneva show a ninefold jump in the number of asylum-seeking Poles arriving in Austria -- their most favored entry point to noncommunist countries -- during the first five months of this year. In West Germany, another favored gateway, the number is said to have roughly doubled this year over the same period last year.

The increases can be taken as an indication of the mounting uneasiness and fear among many Poles about the dramatic course of events and deteriorating economic situation in their country.

The exodus may also be a reflection of what some refugees report has been the easier availability of passports provided by the Warsaw government as part of Poland's general wave of new freedoms.

The influx has become a problem in purely physical terms, however, particularly for Austria, where most of the Poles are lodged while awaiting processing of their immigration requests, usually to the United States, Canada or Australia.

Austrian officials say the main Austrian refugee camp at Traiskirchen and subsidiary camps are already brimming and they have had to scramble to find emergency accommodations for refugees in pension homes and hotels around the country.

At the moment about 3,500 Poles are officially known to be in Austria requesting passage to a new country.Immigration officials say there could be several times that many who have yet to petition the Austrain government for asylum or whose petitions have been rejected.

A spokesman for the Austrian Interior Ministry said the Vienna government, which expects to spend $17.6 million this year to maintain facilities for East European refugees, has formally asked the United States to relax its quota of 4,500 East European immigrants admitted each year. Similar requests have been made of Canada and Australia.

"It's a drop on a hot stone," said International Immigration Committee's Vienna representative, Henri van Weveke, about the U.S. quota. The committee receives financing from 30 member governments to provide transportation for refugees.

According to committee figures 3,366 Poles have registered for asylum in Austria since Jan. 1 this year, compared to 374 in the same period last year. This represents about 75 percent of the total number of East Europeans who have fled here this year.

For Czechs, Hungarians and most other East Europeans, a trip to Austria generally involves a high-risk and illegal border-crossing.But Poland has a special bilateral relationship with Austria permitting two-way travel without visas for the citizens of both countries.

Poland has similar travel arrangement with Sweden, which like Austria is a neutral country but does not have Austria's liberal asylum policy.

West Germany, which does have a liberal policy, reports a sharp increase in the number of Poles seeking asylum this year -- to about 1,300 from January through May -- according to the immigration committee.

The main difficulty for Poles who wanted to travel abroad until now had been obtaining a passport from their own government. Andrew Barco, the head of the Vienna chapter of the Polish-American Immigration and Relief Committee, suspects that Polish authorities may have decided to make passports more easily available in order to encourage immigration with the hope possibly of easing Poland's economic pressures.

In any case, with summer vacation time approaching, Western immigration officials are bracing for a further acceleration of the current trend. "We are preparing now far a rather hot summer," said van Werveke. "We may end up easily with a total of 10,000 East Europeans here looking for asylum by September."

The Poles who have arrived so far are said by officials to come from a broad mix of backrounds, ranging from professors and engineers to the unskilled and uneducated. Barco said a number of former Polish Communnist Party members have also shown up.

The refugees tend to be young. They share a history of economic deprivation, a deep fear about the future of their country and a distaste for communism. But cases of political persecution among the refugees are rare.

Peter Slaski, a 28-year-old physician, fled in February with his wife and 6-year-old son. He had though about leaving for months before and even discussed the prospect with relatives in Baltimore when he visited there last year.

In an interview in a refugee home on the outskirts of Vienna, Slaski said he chose to leave Poland in mid-winter -- several months before his wife could finish her five-year medical training program because "the situation in Poland was bad and getting worse."