Experimentally and theoretically (using mathematical modeling) the combustion of the undeformed porous matrix of cylindrically symmetric forms, in which the active gas reagent is fed from outside through the permeable surface part owing to difference between outside and inside pore pressure in the reaction zone, has been studied. It has been shown that under conditions of the instability of many-dimensional filtration combustion separate cells of exothermic chemical combustion form, which propagated in self-sustained mode. Structure of cellular waves, distribution dynamics and moving direction are determined by totality of factors: temperature field, gas pressure gradients, intensity of exothermic heat release, geometric parameters of porous layer, and heat loss value. The cellular combustion modes of the titanium powder layer were experimentally studied in the circular bath as the flat dish. The comparative analysis of theoretic and experimental results of combustion dynamics of cylindrical sample under cellular mode is given.