In this paper, throughput of two-way relaying under buffer constraints is studied. In the two-way relay system, source nodes initially send their messages to the relay in the multiple-access phase. Relay decodes and stores the messages from different sources in different buffers and subsequently broadcasts a superimposed signal. It is assumed that both source nodes and the relay operate in the presence of statistical queueing constraints. Under these assumptions, arrival rates that can be supported in this system are investigated through the logarithmic moment generating functions of the arrival and service processes. In particular, after identifying the service rates in the multiple-access and broadcast phases and addressing the stability conditions, characterizations of the maximum arrival rates are provided in terms of system resource allocation parameters, signal-to-noise ratios, and quality-of-service exponents. Impact of different parameters on the performance is investigated through numerical results.