This work presents numerical simulations for methane-air combustion within open-cell ceramic radiant plates. The radiant plates are composed of two kinds of periodic repeatable structure elements termed as either the Kelvin cell or the W-P cell. A 3D numerical model considering gas and solid phases, which includes fluid flow, energy/species transport, solid-to-solid radiation, as well as methane-air combustion kinetics, is proposed and fully solved on the pore scale. The effects of cell strut diameters on the flame temperature, solid skeleton temperature and burner radiation efficiency are analyzed. As a result, for porous radiant plates composed of Kelvin cells, as the strut diameter of cell increases, the temperatures of solid skeleton, and burner radiation efficiency increases, and temperature distribution on radiant plate becomes more uniform, while the thermal nonequilibrium between two phases gradually weaken. With the same strut diameter, the combustion phenomena in both the Kelvin cell porous structure and the W-P cell porous structure are compared. It is found that, higher solid temperatures and radiation efficiency of burner can be obtained with Kelvin cell structure, meanwhile, the temperature uniformity of radiant plate with the Kelvin cell structure is better. This indicates that the Kelvin cell structure has a better serviceability.