Highly underexpanded axisymmetric jet was simulated using the Runge-Kutta Discontinuous Galerkin (RKDG) finite element method, which, based on two-dimensional conservation laws, was used to solve the axisymmetric Euler equations. The computed results show that the complicated flow field structures of interest, including shock waves, slipstreams and the triple point observed in experiments could be well captured using the RKDG finite element method. Moreover, comparisons of the Mach disk location exhibit excellent agreements between the computed results and experimental measurements, indicating that this method has high capability of capturing shocks without numerical oscillation and artificial viscosity occurring near the discontinuous point.