The problem of network reliability calculation is studied. It is assumed that a network has unreliable communication links and perfectly reliable nodes. The diameter-constrained reliability for such a network is defined as probability that every pair of terminals of network is connected by operational paths with a number of included edges less or equal to a given integer. The problem of computing this characteristic is known to be NP-hard, just like the problem of computing the network connectivity probability. For solving this problem, we propose the parallel method, which is based on the well-known factoring method. The analysis of the numerical experiments allowed us to set some important parameters of the algorithm to speed up calculations.