The numerical modeling of physical processes in media with micro inclusions requires a tremendous amount of computer memory and CPU time. To solve such multiscale problems there are specific numerical methods. The one of them is the heterogeneous multiscale finite element method (FE-HMM). The FE-HMM algorithms are naturally parallel. In this paper, we have designed the FE-HMM parallel computational schemes to solve the problems of the electrostatic potential distribution in media with pores and cracks. We demonstrate the efficiency of the method through extensive numerical experiments, which include problems with micro inclusions with different geometry.