In waves dynamics, Generalized Kortewegde Vries (gKdV) equation and Sawada-Kotera equation (Ske) have been used to study nonlinear acoustic waves, an inharmonic lattice and Alfven waves in a collisionless plasma, and a lot of more important physical phenomena. In this paper, the simple equation method (SEM) is used to obtain new traveling wave solutions of gKdv and Ske. The physical properties of the obtained solutions are graphically illustrated using suitable parameters. The computational simplicity of the proposed method shows the robustness and efficiency of SEM.