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According to current regulation, millimeter wave links can only rely on low transmission power, which calls for high gain steerable antenna arrays to generate very directional beams bringing signals of detectable power to the intended receiver. However, beam directionality, jointly with the very limited scattering and diffracting capabilities of millimeter waves, implies high sensitivity to obstructions, which can cause link outage. This article proposes new analytical models for the estimation of the outage probability of millimeter wave indoor and outdoor links, based on the derivation of the distribution of the obstruction length along the beam. To derive the models, we use stochastic geometry and assume randomly located obstructions. The proposed models are used to explore the impact on millimeter wave link performance of a number of parameters such as distance between transmitter and receiver, obstruction shape size, density of obstructions, and carrier frequency and modulated bandwidth. The models can be used to study realistic 2D and 3D scenarios, and are shown to be quite accurate by comparing analytical predictions and simulation results in numerous cases.