A mathematical model is developed to describe the dynamic and pseudosteadystate behavior of chemical vapor infiltration, a process used to fabricate fiber-reinforced ceramic matrix composites. The three-parameter dusty-gas model is used to describe the interaction of mass transport fluxes, partial pressures, and partial pressure gradients in the interior of the porous medium, with the viscous flux related to the total pressure gradient through Darcy's law. The model is applied to study the deposition of SiC via decomposition of methyltrichlorosilane in a porous medium whose structure can be represented by a population of uniformly-sized, randomly-overlapping pores. The results show that use of simplified mass transport flux models can lead to significantly different results, even if the concentration of reactants is low and the effects of the products of the reaction on the deposition rate are ignored. It is also shown that operation of chemical vapor infiltration reactors under pressure pulsing can lead to conversion gradients in the densifying structure by a few orders of magnitude smaller than those seen at the same reaction conditions under constant pressure.