In this paper, we consider the transmit and receive antenna array gain of massive MIMO systems. In particular, we look at their dependence on the number of antennas in the array, and the antenna spacing for uniform linear and uniform circular arrays. It is known that the transmit array gain saturates at a certain antenna spacing, but the receive array gain had not been considered. With our physically consistent analysis based on the Multiport Communication Theory, we show that the receive array gain does not saturate, but that there is a peak at a certain antenna spacing when there is no decoupling network at the receiver. As implementing a decoupling network for massive MIMO would be almost impossible, this is a reasonable assumption. Furthermore, we analyze how the array gain changes depending on the antenna spacing and the size of the antenna array and derive design recommendations.