The theory of network reliability has been applied to many complicated network structures, such as computer and communication networks, piping systems, electricity networks, and traffic networks. The theory is used to evaluate the operational performance of networks that can be modeled by probabilistic graphs. Although evaluating network reliability is an Non-deterministic Polynomial-time hard problem, numerous solutions have been proposed. However, most of them are based on sequential computing, which under-utilizes the benefits of multi-core processor architectures. This paper addresses this limitation by proposing an efficient strategy for calculating the two-terminal (terminal-pair) reliability of a binary-state network that uses parallel computing. Existing methods are analyzed. Then, an efficient method for calculating terminal-pair reliability based on logical-probabilistic calculus is proposed. Finally, a parallel version of the proposed algorithm is developed. This is the first study to implement an algorithm for estimating terminal-pair reliability in parallel on multi-core processor architectures. The experimental results show that the proposed algorithm and its parallel version outperform an existing sequential algorithm in terms of execution time. Copyright (c) 2015 John Wiley & Sons, Ltd.