The authors consider modeling of propagation of an accelerating flame upon ignition of a gas mixture at the closed end of a tube. The calculations performed used the turbulent combustion model based on an equation for the concentration probability distribution density (PDD). The equation was tested for the simpler problem of ignition and propagation of a nonsteady state flame through a preturbulized gas mixture. Finally, even numerical solution of the nonsteady-state two-dimensional problem of turbulent flow of a reacting mixture based on the PDD equation is not possible at present. It is necessary to resort to certain simplifications. These latter, while reducing the volume of calculations, unfortunately lead to an increase in the volume of expressions required to describe the model.