Heave and pitch motion of an oscillating airfoil in uniform flow will cause generation of forwarding thrust. Applying a combination of these two motions on flexible foil, one can increase thrust and therefore the efficiency. This is the way that most fishes and other flying animals uses to consume less energy. In this paper, hydrodynamic forces and efficiency of an oscillating airfoil is investigated. A code is developed based on potential flow formulation in combination with Time Stepping Method (TSM) with nonlinear free shear layer dynamic approach to predict the wake behind the lifting bodies. A linear Morino type Kutta condition has been implemented on panels adjacent to trailing edge. In this methodology, there is no need to define the wake shape before starting the simulation and it is an important feature in treating the hydrodynamics of submerged bodies. To validate the presented algorithm, some test cases were investigated. Comparison of propulsion performance of rigid oscillating foil with flexible undulating in different Strouhal number is the novelty of our research. We observe that in a wide range of frequencies, undulation movements is more efficient than rigid oscillations. The numerical results show a good agreement related to analytical and experimental measurements. © 2017 Elsevier Ltd