The problem of the network reliability calculation is studied. As the network reliability we mean the classical reliability measure, i.e. the network probabilistic connectivity. It is assumed that the network has unreliable communication links and perfectly reliable nodes. The problem of computing this characteristic is known to be NP-hard. For solving this problem, we use GPU (graphics processing unit). The parallel methods for exact calculation and evaluation of the network reliability, based on the associative processor are proposed. The numerical experiments along with comparison with experiments of the network reliability calculation on CPU are presented.