For the first time, a comprehensive study of downward flame spread over glass-fiber-reinforced epoxy resin (GFRER) slabs in oxidizer flow has been carried out experimentally and numerically. Microthermocouples were used to measure the temperature profiles on the solid fuel’s surface and in the flame, and a video camera was used to measure the rate of flame spread (ROS). The ROS was found to be linearly dependent on the oxygen concentration, to be inversely proportional to the slab thickness and not to depend on the direction of the flame spread over the slab. The absence of the influence of the forced oxidizing flow velocity and the weak influence of the GFRER pyrolysis kinetics on the ROS were observed. For the first time, a numerical model of flame spread over reinforced material with thermal conductivity anisotropy was developed on the basis of a coupled ‘gas–solid’ heat and mass transfer model, using modifications of the OpenFOAM open-source code. The sensitivity analysis of the model showed that the thermal conductivity in the normal direction to the GFRER surface had a much greater effect on the ROS than the thermal conductivity along the direction of flame propagation. The numerical results show good agreement with the experimental data on the dependences of the ROS on oxygen concentration, slab thickness and the N2/O2 mixture flow velocity, as well as temperature distributions on the fuel surface, the maximum flame temperatures and the flame zone length.