In this work, we model the transient pyrolysis of a slab of polymer of finite thickness subjected to irradiation in which heat is supplied uniformly to the surface of the polymer. The sample of polymer is located on a substrate. The temperature of the polymer rises and it undergoes pyrolysis when the material reaches a critical temperature. A pyrolysis front then develops as a moving boundary. We investigate the effect of the sample thickness on the regression rate of the moving boundary in the case where no char is formed. The result was presented in terms of the pyrolysis of polyethylene on an aluminium substrate. Further investigation was done on the effect of the formation of a char layer on the regression rate of the moving boundary.