The modelling of the large-scale structure of the heliosphere has made significant progress during recent years. Following hydrodynamic two-fluid approaches taking into account protons and neutral hydrogen, pick-up ions and cosmic rays were in- cluded and magnetohydrodynamic models were formulated. The present-day models are, nonetheless, still not capable to describe a realistic three-dimensional heliosphere, simultaneously including several particle populations as well as the heliospheric and the interstellar magnetic field. However, the recent progress regarding the develop- ment of algorithms and codes for a parallel computing architecture offer the oppor- tunity to make further significant progress. In particular, it will enable us to improve the realistic modelling of the effect of changes in the local interstellar medium on the structure of the heliosphere and, in turn, on Earth, which has received increased atten- tion during recent years. We will report about a new model formulation employing the ZEUS-MP code, i.e. a parallel rewrite of the well-known ZEUS-3D. First test results will be presented.