At multiscale modeling of heterogeneous catalytic reactors there appear systems comprising a large number of equations. The solution of such systems is an arduous task and available algorithms require voluminous computations. A modeling strategy has been suggested for such systems. An effective solution algorithm has been developed for a large class of models based on the application of an identical set of numerical tools such as integro-interpolation method, method of straight lines, a special case of a second-order Rosenbrock method, tridiagonal matrix algorithm or Thomas algorithm on each scale of a multiscale reactor model. Step size control is implemented with account for the rate of change of the variables on each scale. The efficiency and robustness of this algorithm were demonstrated at multiscale modeling of heterogeneous catalytic reactors such as tubular reactors, monolith catalytic reactor, and fluidized bed reactor. When switching between reactor types at multiscale modeling it is not necessary to modify the algorithm. The algorithm can also be used for multiscale modeling of heterogeneous catalytic reactors of other types.