Detailed analysis of mathematical modeling of the processes of multiphase media dynamic behavior has been carried out. The basic shortcomings of the current theories are revealed, and the ways to eliminate the same are presented. Mathematical models of the processes occurring in multicomponent systems with nano-fillers, based on the various rheological equations of state, have been developed. Computer programs to implement the mathematical models on the basis of MathCAD package have been compiled. Materials of the work contain extensive illustrative materials that allow for deep understanding of the processes occurring in multiphase media.