Stock prices tumbled today as investors chafed under sky-high interest rates and worried about a potential Soviet invasion of Poland.

The Dow Jones industrial average of 30 big stocks declined 22.53 points to 933.70. The decline in stock prices was broad-based. Only 194 stocks traded on the New York Stock Exchange gained in price, while 1,529 declined. Last Monday the Dow average fell 23.89 points.

On the American Stock Exchange, the overall price decline was the third worst since the exchange began compiling its index in 1973. The Amex index was off 12.90 points to 342.27, with 74 issues gaining in price and 625 declining.

Prices fell sharply in the over-the-counter market as well.

Jerry Hinkle, chief trader for the brokerage firm Stanford C. Bernstein & Co., said that rising interest rates are the chief cause of the decline in stock prices but said that in the last week and a half there has been a general "change in psychology" among investors. In the euphoria following the election of Ronald Reagan, stock prices took off as investors shrugged off all bad news, but over the last two weeks reality seems to have taken hold again.

Hinkle noted that oil company stocks, which had led the increase in the market as a whole, have been particularly vulnerable during the last week, and reports that Ford Motor Co. is borrowing heavily and that Chrysler Corp. is losing money again have added to investor jitters.

But the main source of continuing investor concern is rising interest rates, which threaten to choke off the economic recovery, if they have not done so already, as well as make it harder for investors to afford to buy stock on credit.

The prime rate touched 19 percent last Friday, and most analysts expect it to hit the 20 percent record of last spring within a matter of days. Short-term borrowing costs for banks continued to rise steeply today as the Federal Reserve Board continued to pursue a stringent monetary policy in its efforts to hold down the growth of the money supply to fight inflation.

Volume of the New York Stock Exchange continued heavy today, as 53.8 million shares exchanged hands, up from 52 million on Friday.

Stock prices began the day lower and fell almost without stopping until the final 4 p.m. bell. Reports that some U.S. troops in Europe had been put on alert because of the potential Soviet invasion plus reports that the U.S.S.R. was moving divisions through Poland, supposedly en route to East Germany, merely heightened the tension in an already worried stock market.

Exxon Corp. declined 2 1/8 to 78 1/4, Texaco fell 1 7/8 to 45 l/4 and Occidental Petroleum slipped 1 1/8 to 34 5/8.

Most of the big technology stocks fell, too. International Business Machines declined 1 1/2 to 66 1/4, NCR Corp. was off 1 3/8 to 66 3/4, Xerox fell 1 7/8 to 60 3/8, and International Telephone & Telegraph dipped 1 1/4 to 28 3/4.

The NYSE composite index lost 2.04 points to 75.12, Standard & Poor's index of 400 industrial stocks dropped 4.02 points to 149.17 and the S&P 500-stock composite lost 3.42 points to 130.61.

The American Stock Exchange market value index tumbled 12.90 points to 342.27.

In over-the-counter trading, the NASDAQ composite index lost 7.15 points to 195.87.