Random spatial network models have been recently utilized in the performance analysis and system design for multi-cell networks. Such an approach has been mainly adopted to investigate the outage based system performance, such as the outage probability and outage throughput. However, these performance metrics are defined with a fixed-rate transmission, and cannot characterize the performance of data traffic, which normally adopts rate adaptation. In this paper, we will evaluate the average throughput of a space division multIPle access (SDMA) based cellular network by considering stochastically distributed base stations (BSs) and mobile terminals (MTs). The major difficulty for the performance analysis is the complicated distribution of the interference links. We shall provide an analytical framework for evaluating the average throughput by using the Moment Generating Function (MGF) based method. Simulations will show that the proposed method is very accurate. In particular, the analytical result can be utilized to determine the optimum number of MTs to be served in SDMA networks that can maximize the network throughput.