A Lagrangian-Eulerian simulation technique has been applied to model viscoelastic extrusion flow. The essential feature of our method is to track explicitly the motion of fluid elements in a Lagrangian fashion and to solve fluid fields on a comoving grid in an Eulerian manner at each physical time step. The method is able to track the details of fluid, e.g. deformation and stream line, and also to advance free surfaces in a physical way. Results are presented for the time-dependent flow from rest of both Oldroyd-B and PTT (Phan-Thien and Tanner) fluids, through a planar 2:1 abrupt contraction and in free jet flows.