This paper presents a finite-volume approach with a hybrid flexible distributed/shared memory parallel programming model to simulate the injection mold filling process. The simulation program deals with a three-dimensional nonisothermal, non-Newtonian flow with moving interfaces. The finite-volume method is implemented to solve the governing equations, while a compressive interface capturing scheme for arbitrary meshes (CICSAM) is used to track the advancing melt fronts. For parallel computing, the program implements the "greedy algorithm" as the domain decomposition method to distribute the computational work equally among the different computational nodes, and the message passing interface is used to communicate and exchange information between the computational nodes. For the symmetric multiprocessing nodes, OperMP directives are integrated in the application's loop constructions. This approach effectively improved the solution efficiency in terms of computational time and accuracy. Three-dimensional mold filling examples, which were used to verify and validate the numerical implementation and to demonstrate its performance and capabilities, are presented. (c) 2007 Wiley Periodicals, Inc.