Abstract: Two-dimensional mathematical model of Lurgi tube-shell type methanol synthesis reactor with by-product steam was established, with taking hydrogenation of CO and CO_2 as the independent reactions and methanol and CO_2 as the key components in the methanol synthesis system. The concentrations and temperature profiles in axial and radial direction inside the reaction tubes were obtained by two-dimensional orthogonal collocation method. This method was comparied with finite difference method. The former is better than the later for solving the partial differential equations.