A heterogeneous model for ignition and combustion of cylindrical free-gas samples with a gas-permeable and impermeable surface, including the description of structural and phase transformations is formulated. The effective method for numerical model research, taking into account a zonal structure of combustion wave is offered. Dynamics of porous structure forming of products from a stage of ignition up to the steady mode of exothermal reaction front propagation is considered. The calculated stationary combustion rate and elongation of a burned specimen versus its diameter, particle size of a fusible component, initial porosity and pressure of inert gas are received. Experimental data are qualitatively compared with calculated ones. The change in characteristics of combustion wave in a non-stationary mode is analyzed. The structural oscillations resulting in lamination of a porous specimen in a zone of synthesis products in a self-oscillatory combustion mode are found out. The factors, which are the reason for structural oscillations occurrence are determined. Modeling for mechanical compression of a sample shows that a stabilizing effect on the process of combustion consists of additional compensation of loosening forces.