Due to the importance of signature vector in studying the reliability of networks, some methods have been proposed by researchers to obtain the signature. The notion of signature is used when at most one link may fail at each time instant. It is more realistic to consider the case where non of the components, one component or more than one component of the network may be destroyed at each time. Motivated by this, the concept of t-signature has been recently defined to get the reliability of such a network. The t-signature is a probability vector and depends only on the network structure. In this paper, we propose an algorithm to compute the t-signature. The performance of the proposed algorithm is evaluated for some networks.