A Monte Carlo (MC) technique involving explicit calculation of molecular trajectories in fibrous media is used to obtain effective transport coefficients in the Knudsen regime of gas diffusion. A fully penetrable cylinders (FPC) model is used to represent a fibrous substrate during the course of densification, as in composite fabrication processes such as chemical vapor infiltration (CVI). The calculated Knudsen permeabilities are in excellent agreement with available data. Accessible porosities are computed as a function of total porosity and are shown to depend on the fiber number density. The nonfiber phase is shown to percolate at ϕ ≈ 0.095, but the threshold is sensitive to the boundary conditions employed.