Abstract: In this talk, we discuss the global stability of  the  Minkowski spacetime  in the wave  coordinates  system for the massive Einstein-Vlasov system. In particular, compared with previous results by Lindblad-Taylor, in which the Vlasov part is assumed to have compact support assumption, and Fajman-Joudioux-Smulevci, in which the spacetime is assumed to be exact Schwarzschild in the exterior region,  we do not impose  any compact support condition for the Vlasov part and   allow a   large class of non-isotropic perturbations for the metric part, which decay at rate $\langle r\rangle^{-1+}$ towards space infinity.