We introduce a model of combustion of porous samples in a gravitational field, in which the high temperature products can deform, to describe the synthesis of high porosity materials and its dependence on parameters of the problem. In addition to the main synthesis reaction we allow for the possibility of a gasification reaction of a special additive. We derive an equation for the elongation of the sample due to an increase in its porosity, which is caused by the additional gas produced in the main reaction or in the additive reaction or both. We also carry out numerical simulations of the model and compare to existing experimental results. We describe ignition, propagation, extinction and stability of propagating combustion waves and their dependence on various factors such as heat loss, gravity, rheological parameters and amount of additive. In particular, we show the possibility of synthesizing uniform high porosity materials in a microgravity environment.