Three-dimensional simulations of laminar flame propagating downwards the vertical surface of a rigid polyurethane slab heated by a radiative panel are presented and compared with the measurement data. The gas-phase model (ANSYS Fluent) allows for finite-rate volatile oxidation, soot formation and oxidation, emission, transfer, and absorption of thermal radiation. The solid-phase model Pyropolis considers heat transfer across the material layer and generation of combustible volatiles in thermal decomposition of the material. Kinetic model of material decomposition is derived to obey the microscale combustion calorimetry data for different heating rates. Transient behavior of propagating flame and pyrolysis zone, as well as spatial distributions of heat flux components, temperature, and mass burning rates over the specimen surface are examined. Variation of the thermal properties of the material during its thermal decomposition, as well as the specimen surface emissivity and reradiation are shown to be the important issues strongly affecting model predictions. Two distinct modes of counterflow flame spread, thermal and kinetic, are identified. In the thermal mode corresponding to fast chemistry in the gaseous flame, the flame propagation velocity is governed by the heating rate of the combustible material ahead of the flame front. Alternatively, in the kinetic mode, it is limited by the burning velocity of the volatile-air mixture forming ahead of the flame front. Simulation results are favorably compared with the measured propagation velocity.