In this paper, we investigate a reconfigurable intelligent surface (RIS) aided multi-pair communication system, in which multi-pair users exchange information via an RIS. We derive an approximate expression of the achievable rate by assuming that statistical channel state information (CSI) is available. A genetic algorithm (GA) to solve the rate maximization problem is proposed as well. In particular, we consider implementations of RISs with continuous phase shifts (CPSs) and discrete phase shifts (DPSs). Simulation results verify the correctness of the obtained results and show that the proposed GA method has almost the same performance as the globally optimal solution. In addition, numerical results show that three quantization bits can achieve a large portion of the sum achievable rate for the CPSs setup.