Methods to animate multiphase fluids are rarely researched, although such phenomena are common in our daily lives. The main focus of this research is to develop a suitable method to create realistic animation of multiphase flows, i.e. flow of fluid mixtures. Our method is based on Navier-Stokes equations, a set of physical equations that describe motion of fluid. A Marker-and-Cell (MAC) grid is used to solve the equations on discrete computational domain. To simulate several fluids, we propose the modification of Volume-of-Fluid (VOF) representation of fluid and integrate it into the multiphase-fluid approach. A mixture of fluids is treated as a single fluid having variable density and viscosity. This scheme allows two or more fluids having different densities and viscosities to be simulated simultaneously.