The two-phase mathematical model was developed for the cylindrical axial flow reactor with the stationary catalyst layer for one irreversible reaction. Block converter and converters with stationary catalytic layer in the cyclic space between two co-axial cylinders at radial reagent flow (cylindrical radial flow reactor) are used for purification of exhaust gases. The two-phase mathematical model for cylindrical radial flow reactors for one irreversible reaction and complex reactions as well as two-phase mathematical models for block converters of the honeycomb structures and co-axial cylindrical converters for complex chemical transformations are under development.