Numerical modeling of gas and liquid flows and, in particular, multiphase mediums, is a promising direction of scientific investigations and development of industrial apparatus. The experimental approach in the field of multiphase flows does not always allow obtaining the required information about the flow structure due to the excessive amount of physical phenomena involved. Numerical simulations of real flows with inclusion of all processes and phenomena or on real-scale geometries are very resource-demanding and are not feasible on stand-alone personal working stations. Thus, applying parallelization techniques for the existing solution algorithms with the means of the OpenMP library alongside supercomputer technologies can reduce computational time and can help with simulations of complex flows. The study presents the description of the previously developed mathematical model of polydisperse multiphase flows, a numerical algorithm for the solution of the governing equations of the model, description of the numerical method and technique of conducting the numerical experiments. The results presented in the paper have been obtained during numerical experiments carried out at the Politekhnichesky SC, and comprise the dependencies of program working time on the amount of threads and model parameters.