Millimeter wave (mmWave) communications has been considered as a promising technology for 5G cellular networks. Exploiting directional beamforming using antenna arrays to combat path loss is one of the defining features in mmWave cellular networks. However, previous works on mmWave network analysis usually adopt simplified antenna patterns for tractability. In this paper, we show that there are huge discrepancies between the simplified and actual antenna patterns when investigating the coverage probability of mmWave networks. Analytical expressions for the coverage probabilities are derived using tools from stochastic geometry, by considering the actual antenna pattern with the uniform linear array. Moreover, the impact of the array size is investigated, which cannot be revealed from existing results with simplified antenna patterns. Numerical results will show that large-scale antenna arrays are required for satisfactory coverage in mmWave cellular networks. Furthermore, dense mmWave cellular networks are shown to achieve much higher rate coverage than conventional sub-6 GHz cellular systems. © 2016 IEEE.