A parallel version of the program for the simulation of flows in the Earth's mantle has been developed. A non-stationary model of the mantle flows describes a compressible medium with strongly varying rheological and transport properties. It is based on the solution of the Navier–Stokes equations. The numerical model includes both explicit and implicit finite difference schemes implemented by vector fitting. The parallel algorithm has been analyzed in detail. The parallel algorithm provides nearly linear acceleration, despite the use of vector fitting. The main characteristics of the parallel algorithm are presented. The total time computation and the inner loop for a given accuracy of calculation varying for different sizes of grid spaces have obtained. The inner loop is used to compute the mantle flow velocities along the coordinate computing space. The dependence of speedup and efficiency on the size of the grid computing space is shown. A weak dependence of these parameters on a specified accuracy of the calculations is shown. The description of the process of melting and diapirism in the lower crust is obtained by calculations on a multiprocessor system. The structure of the floating granite magma has been determined.