Stock prices are different on a daily basis with small ups, small downs, or abrupt changes. While small fluctuations are typical according to economic theory and understandable to most investors, abrupt changes are unexpected and can be either harmful (if dramatic downward change occurs) to a society's economy (and investors) or beneficial (if vast upward change occurs) to a society's economy (and investors). We introduce the variance change point model (volatility change point model), and use it to analyze two stocks: Shanghai Stock Composite Indices and Shenzhen Stock Composite Indices from 1992 to 2002. The authors use a binary procedure combined with Schwarz Information Criterion (SIC) as in Chen and Gupta (1997) to search all the possible variance (volatility) change points exist in the sequence. Changes in both indices are successfully identified and their economic explanations are given.