Abstract <p>This article develops a mathematical model of an unsteady process in a catalyst layer with cylindrical grains. The model includes diffusion–reaction–convection equations, an equation for calculating the rate of forced convection in grain pores, the heat conductivity equation for the catalyst skeleton, and the equations of heat and mass transfer of gas in the catalyst layer. A computational algorithm based on splitting by physical processes is constructed for the developed model. The tasks of chemical kinetics are separated into an isolated integration stage and solved by the RADAU5 method with an adaptive step. The diffusion–reaction–convection equations are hyperbolized to reduce the estimated time of slow diffusion processes in grain pores. A three-layer scheme explicit in time is used for these equations. The heat conductivity equation is also explicitly integrated, and the integral source term in it is calculated using the trapezoid method. The transport equations along the length of the catalyst layer are integrated implicitly to expand the range of the algorithm’s stability in the case of sharp temperature and concentration fluctuations in the layer. The boundary conditions for the catalyst grain are approximated by second-order spatial accuracy. The constructed algorithm is tested on a problem with a known analytical solution and compared with the solution of the Dirichlet problem in a mathematical package. The developed model and algorithm are used to study the modes of a real unsteady process in the catalyst layer.</p>