Thermal conductivities were calculated for the refractory brick of carbon-alumina-pore system, carbon-alumina-silicon carbide-pore system and carbon-alumina-silica-pore system. The proposed conduction model was extended from our previous two phase conduction model developed for solid material with particulate inclusion. The three or four phase model reflects the microstructure of the refractory brick and predicts the maximum and minimum conductivities in parallel and perpendicular directions to c-axis of graphite. The calculated values were plotted in the triangle of thermal conductivities of graphite-alumina-pores systems as functions of alumina content and porosity. The thermal conductivity of reflactory brick along perpendicular direction to c-axis of graphite decreases at higher fractions of alumina grains and pores. This calculated result is explained by the decrease of volume fraction of graphite with a higher thermal conductivity. The experimental thermal conductivities were measured in the range predicted from the calculation and very close to the average value of calculated maximum and minimum conductivities.