AbstractThe torus network is one of the most popular interconnection topologies for massively parallel computing systems. In this paper, we mainly consider the p-panconnectivity of n-dimensional torus networks with faulty elements (vertices and/or edges). A graph G is said to be p-panconnected if for each pair of distinct vertices u,v∈V(G), there exists a (u,v)-path of each length ranging from p to |V(G)|−1. A graph G is m-fault p-panconnected if G−F is still p-panconnected for any F⊆V(G)∪E(G) with |F|≤m. By using an introduction argument, we prove that the n-dimensional torus T2k1+1,2k2+1,…,2kn+1 is ∑i=1nki-panconnected and (2n−3)-fault [∑i=1n(ki+1)−1]-panconnected.