Using numerical experiment one-dimensional unsteady processes of heterogeneous combustion in porous object under free convection in horizontal case have been investigated and compared with vertical case. It is shown that in the case of the horizontal porous object the oxidizer supply,which is the result of natural convection,is not sufficient for the appearance of stable wave of heterogeneous combustion. In contrast to the vertical position of the object,there are no longlived combustion waves in the horizontal case,which completely burns down the solid combustible material. When the ignition zone is on the border of the object,the combustion wave near the vicinity of the boundary burns the oxygen and becomes extinct. When the ignition zone is in the center of the porous object,two combustion waves arise which may move very slowly,burn oxygen and become extinct.