Abstract: The growing size of the multiprocessor system increases its vulnerability to component failures.The minimum size of a largest connected component can be regarded as a measure of fault tolerance of the network，which provides a complement to the vertex connectivity.In order to make a full evaluation，it is essential to estimate the minimum size of a largest connected component providing a lot of failing processors（vertices） which yield a disconnected surviving network.This paper analyses the fault tolerance of Pancake network，and shows that if F is a set of vertices in Pn with |F|≤kn-3k+1（k=2，3），Pn-F has one largest connected component with at least n!-|F|-（k-1） vertices，and the remaining small components have at most k-1 vertices in total.