In the past few years, lots of techniques were developped for modeling dynamic crack growth. One of the main difficulties is that the discretization of the problem is time dependent. This can produce numerical instabilities, uncontrolled energy tranferts and high frequency oscillations in the solution due to time discontinuities in the numerical model. This paper proposes, in the framework of the eXtended Finite Element Method (X-FEM), a study of Time Discontinuous Galerkin Method (T-DGM). Combining efficient tools like X-FEM and T-DGM , the obtained results are well accurate and will allow to check efficiency for crack initiation, growth and arrest criteria.