Multidimensional (2D and 3D) chemical vapor infiltration models are formulated and used to simulate densification of isotropic or anisotropic preforms of various geometries using Sic deposition from methyltrichlorosilane. A generalized form of the dusty-gas model for mass transport in anisotropic porous structures is used as a flux model in the pore space, and the multidimensional model equations are solved using the Galerkin finite element method. Structures consisting of freely overlapping fibers parallel to a Line (one-directional), parallel to a plane (two-directional), or without preferred orientation (three-directional) are employed to model the microstructure of the preforms. The obtained results show that the effects of preform geometry can lead to partial pressure and deposition profiles in the preform that are considerably different from those suggested by one-dimensional analyses of the chemical vapor infiltration process.