A mathematical model of the infusion process in producing reinforced articles is proposed. The model is based on the analysis of flow of a Newtonian liquid inside a rectangular multilayer channel. According to the model, a liquid enters the central (feeding) layer, moves through this layer, and simultaneously impregnates peripheral layers. So, the flow is two-dimensional. Flow inside the porous layers is treated in terms of the Darcy equation with different permeability coefficients in two directions, Principal solutions for the flow front development and pressure evolution were obtained and analyzed, Then the initial model, developed for a Newtonian liquid, is generalized for the so-called "rheokinetic" liquid. which changes its rheological properties in time as a result of temperature variation and/or any possible chemical process, in particular, the reaction of curing of a binder. It was proven that in this case the solution is automodel. This means that the solutions obtained for a Newtonian liquid in the dimensionless form are valid for an arbitrary rheokinetic Liquid.