This work presents a novel mathematical model of unsteady processes in a catalyst layer with cylindrical grains and a parallel computational algorithm for its solution. The model describes unsteady diffusion-reaction dynamics in an axisymmetric two-dimensional formulation. The thermal conduction equation for the catalyst skeleton is derived by averaging the heat transfer equation over a grain under isothermicity assumptions. Catalyst granule heating is represented as the volumetric integral average over the pellet volume. The computational algorithm employs the finite-volume method, with the source term expressed as a multiple integral and computed via the trapezoidal rule. Chemical kinetics follow a single-step reaction mechanism. Convergence analysis demonstrates the need for sufficiently fine spatial discretization. To accelerate computations, hybrid MPI/OpenMP parallelization is implemented, enabling performance testing on both high-performance clusters and personal computers. The problem’s spatial characteristics influence the choice of optimal parallelization strategy, with efficiency analysis revealing performance variations across grid resolutions. As a practical application, the model simulates oxidative regeneration in cylindrical-grain catalysts, with numerical results effectively capturing transient process features.