Motivated by the design of fault-tolerant multiprocessor interconnection networks, this paper considers the following problem: Given a positive integer t and a graph H, construct a graph G from H by adding a minimum number A(t,H) of edges such that even after deleting any t edges from G the remaining graph contains H as a subgraph. We estimate A(t,H) for the torus, which is well-known as a very important interconnection network for multiprocessor systems.