This paper develops two aspects improving crack propagation modeling with the X-FEM method. On the one hand, it explains how one can use at the same time a regular structured mesh for a precise and efficient level set update and an unstructured irregular one for the mechanical model. On the other hand, a new numerical scheme based on the X-FEM method is proposed for dynamic elastic-plastic situations. The simulation results are compared with two experiments on PMMA for which crack speed and crack path are provided.