A hybrid two-/three-dimensional solution technique is presented to model 3-D flow fields in resin transfer moeling using Darcy’s law. The 3-D flow field is only solved for regions where all three velocity components are significant, thus largely reducing the number of unknowns, Elsewhere, the commonly used 2-D approximation for flow in thin gaps between plates is employed. The method Is applied to regions where the flow splits, such as T-joints. Because of the uncertainties associated with an accurate determination of the permeability in these regions, a simplified, decoupled procedure is proposed, which reduces the computational complexity. In this procedure, the flow front is advanced using the 2-D formulation. The 2-D formulation also provides the boundary conditions for the subsequent computation of the 3-D flow field without feedback of flow field information to the 2-D model. The governing equations are solved using boundary fitted coordinate systems (BFCS) together with the finite difference method (FDM). Numerical as well as algebraic grid generation and domain decomposition are employed to generate grids that always coincide with the continuously deforming and enlarging flow domain. Results that include the tracking of numerical tracer particles to visualize the three-dimensionality of the flow field are presented for isothermal flow of a Newtonian fluid through a T-joint. This detailed flow field description is expected to form the basis for a rather accurate simulation of quantities that largely depend on the fluid particle pathlines, such as the degree of cure. The method is also extendable to shear-thinning fluids as well as to 3-D flow in the vicinity of the flow front.