Thermal energy collisions of two p-excited alkali-metal atoms have been examined, taking into consideration the fine-structure splitting of atomic energy levels. Collisional-induced transitions between fine-structure levels and energy-pooling processes have been investigated by means of combined semiclassical approximation ͑CSA͒. The operator of evolution was constructed with the aid of a numerical solution of a time-dependent quantum electronic equation with appropriate asymptotic Hamiltonian and single trajectory approximation for nuclear motion at large internuclear separations R. Generalized multichannel Landau-Zener model with adiabatic phase averaging for small R has been included in CSA. Numerical results for cross sections in case of scattering of two 3p-excited sodium atoms in a collision energy range of 300-2000 K have been obtained. The estimation of results accuracy was carried out. The propensity rule for detailed collisional-induced finestructure transitions has been established.