The present paper investigates a problem on modelling of internal heat-mass transfer and deforming processes in porous elastomer materials ablating under high temperatures and withstanding finite deformations (up to tens of percents). Attention is mainly paid to investigation of the effect of finite deformations on kinetics of heat transfer and mass transfer of gases in pores in the presence of an inner source of gas generation (e.g. pyrolysis of elastomer phase). It is shown that mathematical statements of the problems on internal heat-mass transfer and deforming in case of finite deformations are coupled. The following phenomena result from this coupledness : growing pore pressure of pyrolytical gases and cooling the material in mechanical compression, the appearance of tensile shrinkage stresses near the heated surfaces of the material. All the effects are investigated numerically.