Abstract: The international financial markets turmoil, which started around mid-2007, has depreciated substantially since August 2008. The financial market crisis has led to the collapse of major financial institutions. Nevertheless, crashes and/or crises are not devoted to only developed markets and developing countries including India, are not excluded from this rule and it may face such a condition.  The sharp decline of Sensex price index from its closing peak of 20,873 on January 8, 2008, to less than 10,000 by October 17, 2008, in line with similar large declines in other major stock markets is good reminders of this fact.  Volatility as a measure of risk plays an important role in many financial decisions in such a situations. The main purpose of this study is to examine the volatility of the Indian stock markets and its related stylized facts using ARCH models. The BSE500 stock index was used to study the volatility in the Indian stock market over a 10 years period. Two commonly used symmetric volatility models, ARCH and GARCH were estimated and the fitted model of the data, selected using the model selection criterion such as SBIC and AIC. The adequacy of selected model tested using ARCH-LM test and LB statistics. The study concludes that GARCH (1,1) model explains  volatility of the Indian stock markets and its stylized facts including volatility clustering ,fat tails and mean reverting satisfactorily.