The dependence of stock prices on time is analyzed during major stock market crashes from the beginning of the 1929 Wall Street Crash to recent financial crises. A model of stock price dynamics is presented to describe the stock price decline during stock market crashes. It is shown from daily stock price data that stock price dynamics can be described by two processes. In the fist process, the selling-off decision by investors is driven by the negative available information and not from the negative stock performance information. During the first process, the daily stock price is inversely proportional to the length of the period of the stock price decline. For the second process, the sharp price decline is explained by the panic chain process of the crowd, whereby new information about the stock price decline causes an initiation of the new selling-off of the shares, resulting in an exponential stock price decay. The model explains stock market crashes and sharp stock price declines for Dow Jones (1929), Enron (2001), Lehman Brothers Inc. (2008), Wachovia (2008), Washington Mutual (2008), Citigroup Inc. (2008), AIG (2008).