An attempt was made for the first time to model the pressureless infiltration of a porous preform, from first principles, as flow through a porous medium. To this end, a transient, two-dimensional, laminar flow model in a cylindrical polar coordinate system has been developed to predict the flow phenomena in the molten alloy-porous ceramic filler material system. Two different modeling approaches were considered for the porous preform, and their relative accuracy/adequacy was assessed for predicting the infiltration rate (i.e., composite growth). The sensitivity of model predictions to various assumptions and numerical approximations, such as the initial preform wetting height, gridsize distributions, and time-step size, were tested computationally. For a first approximation, a structure-sensitive parameter (β) on the order of 10−4 m, which is the same as that reported in the literature, gave reasonably accurate results. A hypothetical computation which assumed no nitride formation provided an activation energy value of 18 kJ/mol for a surface tension-driven infiltration process. In addition to these, the influence of process parameters such as particle size and operating temperature on the predicted results was investigated numerically and was shown to compare well with experimentally obtained data.