The computational modeling of crack propagation is important in aerospace and automotive industries because cracks play a significant role in structural failure. In comparison with the quasi-static case, inertial effects are significant in dynamic crack propagation. The classical numerical tool for modeling dynamic crack propagation is the standard finite element method (FEM). However, the method suffers from problem of mesh-dependency. Enriched finite element procedures such as the eXtended/Generalized finite element method (X/GFEM) are able to solve this issue by adding enriched degrees of freedom (DOFs) to nodes of the original mesh, thereby providing full decoupling between the mesh and cracks. Yet, X/GFEM suffers from other issues that are inherent to the formulation such as the need for more complicated methods for applying non-zero Dirichlet boundary condition, and an intricate computer implementation. In the thesis, the Discontinuity-Enriched Finite Element Method (DE-FEM) is used to simulate dynamic crack propagation as an alternative to X/GFEM. DE-FEM also decouples cracks from the background mesh while solving X/GFEM’s aforementioned issues. This is achieved by adding enriched DOFs along cracks. Prescribing non-zero essential boundary conditions is as straightforward as in standard FEM. Moreover, DE-FEM’s enrichment strategy provides simplicity on crack propagation, as the crack tip node can be transformed into a crack segment node directly with little effort. Also, fewer enriched DOFs than in X/GFEM are appended while advancing cracks. In the numerical examples of either stationary crack with dynamic loading or dynamically propagating cracks, DE-FEM is able to reproduce analytical and/or experimental results. Both Bathe’s time integration method and the classical Newmark constant average acceleration method are applied and compared. Results show DE-FEM is a suitable candidate to solve dynamic fracture problems.