The basic thrust of this article is to examine how shocks and volatility are transmitted across sector indices. This article employs the autoregressive asymmetric BEKK-GARCH model. The study is based on daily data from the National Stock Exchange (NSE) of India from January 2004 to January 2014. Volatility spillover was found to be bidirectional among the two pro-cyclical sectors: Finance and IT. But, there was a unidirectional shock and volatility spillover from the non-cyclical FMCG sector to both the pro-cyclical sectors. The FMCG sector has remained almost unaffected by the spillover from the other sectors. Moreover, the evidence of asymmetric spillover has been found to be present in most of the case. Second, correlations between the sectors were found to be higher during the period of global financial crisis. But no such evidence was found in the context of the Euro zone debt crisis. Understanding the dynamics of shocks and volatility transmission is necessary for risk management in general and for optimal portfolio allocation and hedging strategy in particular. To the best of our knowledge, this is the first study on Indian stock market which has analysed the dynamics of shock and volatility transmission across sector indices.