In this paper, we derive the outage probability in directional millimeter-wave communications, capturing the effect of beamforming. In the proposed scenario, multiple transmitters are spatially distributed according to a spatial Poisson Point Process, which can cause interference to a pair of transmitter/receiver communicating nodes. The analysis considers a general distance-based path loss with Rayleigh and Rician fading channels and a sectored antenna model. Assuming that nodes are uniformly distributed over a circular or annular area centered at the receiver, we derive the outage probability due to the aggregate interference caused by multiple transmitters. The outage probability is based on the Signal-to-interference-plus-noise ratio (SINR) derived for the transmitter/receiver pair. Several simulations confirm the effectiveness of the derived results for different wireless channels and beamwidth values, highlighting the effect of directional communications on the outage probability.