In this paper, we present a close-form expression for the downlink throughput of a massive MIMO system with finite antenna elements in a multi-celluar systems. In practice, the performance of massive MIMO system is limited by the number of antenna elements. From the operator aspect, the cost of massive MIMO is a major concern. Thus, a massive MIMO system with finite antenna elements is of interest. On the other hand, as the number of antenna elements is not so large, the impact of co-channel interference from neighboring cells become a critical issue that should be taken into account. We consider the time-division duplexing (TDD) multi-celluar systems. Our system model accounts for the effects of channel estimation, pilot contamination, 2D channel and 1D antenna array, and our simulations take 3D channel and 2D antenna array into consideration in addition. We derive approximations of achievable rates with linear precoders, and validate by simulations. Our results can provide an evaluation framework for designing a practical massive MIMO system to find the performance tradeoff between the number of antenna elements and cost.