An equivalent continuum approach was used to model the heat transfer in the array of channels of a non-adiabatic monolith reactor. The equivalent solid thermal conductivity in the transverse direction was derived for different cross-sectional geometries of the channels. The partial differential equations modeling the heat and mass transfer in a non-adiabatic reactor were solved numerically. The combined global collocation and collocation on finite element method was used to solve for the steady state solutions. And the backward finite difference method with predictor-corrector modification was added to solve for the time dependent solutions. Simulation results for exothermic and endothermic reactions are presented for ceramic and metallic monolith supports. The effects of channel geometry, channel density, wall thickness, reactor length, inlet fluid temperature and concentration were studied. Results showed that monoliths with triangular channels, higher channel density, thinner wall and longer length gave higher overall conversion for carbon monoxide oxidation. The effect of hydrogen on carbon monoxide oxidation was studied. No multiplicity was found. The simulation results for monolith converter with non-uniform flow qualitively confirmed the experimental observations of others' work.