Computer simulation results are presented for the effective bulk transition, and Knudsen diffusion coefficients in structures consisting of parallel nonoverlapping (impenetrable) or partially overlapping (penetrable) fibers. The numerical procedure is based on a discrete step-by-step random walk mechanism used to determine the mean square displacement of molecules traveling in the interior of the porous medium. The computed transition regime diffusivities are compared with the predictions of the reciprocal additivity effective diffusivity expression. The bulk diffusivity results are also expressed as formation factors describing other transport properties (e.g., thermal and electrical conductivity, magnetic permeability, and dielectric constant) of the fibrous structures or in general of the corresponding arrays of cylinders (either nonconducting or infinitely conducting with respect to the matrix phase). The formation factors of nonoverlapping cylinders are compared with variational bounds and analytical and numerical results of the literature.