The need for time-efficient simulation is increasing in all engineering fields. Potential improvements in computing speeds are provided by multi-core chips and parallelism. However, the efficient numerical integration of systems de- scribed by equation oriented languages requires the ability to exploit parallelism. This paper investigates the problem of the efficient parallelization of hybrid dynamical systems both through the model and through the solver. It is first argued that the parallelism is limited by dependency con- straints between sub-systems, and that slackened synchro- nization between parallel blocks may provide speed-ups at the cost of induced numerical errors, which are theoret- ically examined. Then two methods for automatic block diagonalization are presented, using bipartite graphs and hypergraphs. The application of the latter method to hy- brid dynamical systems, both from the continuous state variables and discontinuities point or view, is investigated. Finally, the model of a mono-cylinder engine is analyzed from equations point of view and a possible split using the hypergraph method is presented and discussed. Conference proceedings at http://www.ep.liu.se/ecp_home/index.en.aspx?issue=084