In this paper, we study two-way multi-relay networks (TWMRNs) in which two nodes exchange information indirectly via an optimal relay node in Rayleigh fading channels. An amplify-and-forward (AF) scheme has been employed and the network mechanism is investigated in depth using a Markov chain model. Automatic Repeat-reQuest (ARQ) retransmission has been applied to guarantee successful packet delivery. The bit energy consumption and goodput are analyzed as functions of the signal-to-noise ratio and transmission rate. Through numerical results, it is demonstrated that selective relaying in TWMRNs can potentially increase the network reliability and achieve higher spectrum and energy efficiency than two-way networks with a single relay.