Abstract-We consider a model of filtration combustion in a thin porous layer immersed in a bath of gaseous oxidizer. which provides for exchange of the oxidizer between the pores and the bath. We employ approximate analytical methods to derive explicit analytical expressions for various quantities associated with uniformly propagating solutions, including the combustion temperature, the propagation velocity, and the final depth of conversion, as well as results about the structure of the solution. We also employ numerical computation to find profiles for the reaction rate, temperature. pressure, density and depth of conversion, as well as to determine the stability of the solutions as a function of various parameters. We identify a new pulsating instability associated with gas mass transfer between the pores and the bath, and describe the mechanism of pulsations.