The method of parallelization of processing in simulations of the Monte Carlo type is proposed and tested on the 3D Ashkin-Teller model characterized by a rich phase diagram. The message passing is applied and the MPI library is exploited. It is demonstrated that the method works well in different regions of the phase diagram, where the phase transitions are first-order and continuous. The dependence of speedup and efficiency on the number of parallel processes is studied. The condition for the best speedup and efficiency in these simulations is formulated and discussed using the results obtained on symmetric NUMA multiprocessor and on symmetric multicomputer. The suggestion as to effective use of the method even in highly heterogeneous computer systems is also given.