Abstract: A numerical simulation of the toroidal shock wave motion in a cylindrical shock tube was carried out using the discontinuous finite element method, which was developed to solve the axisymmetric Euler equations based on two-dimensional conservation laws. The computed results show the complicated flow field, which is formed by shock propagating in the cylindrical shock tube, can be captured efficiently using the discontinuous finite element method. The numerical solutions with steep gradients near the focusing point indicate the discontinuous finite element method has high resolution and there can not lie numerical oscillation and artificial viscosity near the discontinuous point.