This study presents the results of a comprehensive experimental investigation and numerical simulation of the downward flame spread over PMMA slabs. For the first time, in the case of downward flame spread over PMMA slab 9.6 mm thick, temperature and species concentration fields in the gas-phase flame, temperature profiles in the condensed phase and dependence of the heat flux to the burning surface on the distance from the flame front were obtained. A coupled model of heat and mass transfer involving two-dimensional elliptic conservation equations both for gas phase and solid fuel has been used with the fuel surface approximation of the samples burnout. This allowed us to state, for the indefinite intermediate mode (in terms of the sample thickness, which are not neither thermally thin nor thermally thick), a mathematical model ensuring good agreement between the experimental and calculated macro parameters of combustion. The results of comparing the experimental and calculated data allowed us to determine a number of facts, which, despite the satisfactory agreement between the simulation and the experimental data in the main macro parameters, indicate the necessity of further improvement of the model derived. Such facts are: the increasing disagreement between the calculation and the experiment in the position of the maxima of the temperature in the gas phase as the distance from the flame front grows; essential difference in the width of the MMA and O2 consumption zone between the calculation and the experiment; identification in the experiment of CO as an intermediate product. Further improvement of the model should be aimed at more detailed development of the combustion reaction mechanism, which should consider at least two steps.