Theoretical and experimental approaches to the problem of combustion wave stability in gas filtration combustion are described. An approximate criterion of instability for an initially plane combustion wave front is suggested within the framework of a hydrodynamic model. It is shown that the wave instabiliry cannot be observed if the reactor diameter is under a critical value. The critical value of the diameter increases with increasing rate of gas filtration. A combustion wave propagating in the direction opposing the filtration flow is more stable than a cocurrent wave, which is consistant with experimental results.