Hydrodynamic performance of flapping foils for the propulsion or station keeping of near-surface underwater vehicles is examined numerically. The objective of the project is to determine effects of momentum fluxes associated with the vortex wake, radiating waves and their interactions on the thrust and efficiency of the flapping foils. The fully nonlinear viscous flow problem is solved using a finite difference method based on boundaryfitted coordinates. Various flapping foil mechanisms, such as of a single foil, twin foil and hinge-connected double foil, are considered. Results are obtained for a range of key variables such as the Strouhal and Froude numbers, unsteady parameter, and the depth of foil submergence. New results obtained in this work reveal complex interactions between the flap-motion generated waves and vortices, in particular, how the deforming free surface above the vehicle and radiating surface waves could affect the generation and evolution of shed vortices and the thrust-generating capacity of flapping foils. Necessary conditions for high propulsive efficiency are found to be (i) Strouhal number between 0.25 and 0.35 and (ii) oscillation at supercritical frequency, i.e., τ> 0.25. At the critical frequency τ= 0.25 the efficiency is found to be low particularly when the body is very to the free surface. Upstream wave propagation at sub-critical frequency τ< 0.25 results in the loss of propulsive efficiency. Mechanisms affecting the efficiency are amplified by the foil proximity to the surface. In the case of flapping hinged double foil, in-phase oscillation of the foils results in high thrust while out-of phase flapping produces nearly null mean thrust. Flapping of twin foil in the "clapping mode" results in a pulsating wake jet yielding a large thrust but requiring large torque and hence at low efficiency. Efficiencies upto 80% are found in the simulations with single foil. Copyright © 2014 by ASME.