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In this paper, we consider wireless networks with directional antennas using slotted ALOHA medium access control. The channel model incorporates the effects of propagation loss and shadowing with Rayleigh fading. By deriving the cumulative distribution function of the signal-to-interference-and-noise ratio (SINR) of a certain link in the network, the outage probability of the link is analyzed. In particular, the analysis works for the arbitrary beam patterns of the directional antennas used in the networks. Moreover, we propose a new parameter, i.e., the array interference factor, which can characterize the average performance of an arbitrary beam pattern in random wireless networks. This provides an efficient way for designers to evaluate the system performance under different beam patterns. The network throughput and the transport capacity of a random wireless network with directional antennas are also analyzed. It is shown that the network transport capacity is of the same order as the square root of the node density, which conforms with the well-known capacity of wireless networks. The analysis is useful for designers to optimize the system performance of wireless networks with directional antennas.