This work focuses on the hydrodynamic performance analyses of three different types of flapping hydrofoils, in this case the pitch-heave (PH), left-swing (LS), and right-swing (RS) types, in their power extraction regimes via two dimensional CFD simulations. The power extraction performance is presented in an isocontour parametric map and is investigated from a comparison of the kinematics parameters and the development of unsteady vortices among the three types. It is found from the parametric analysis and comparison that the LS-type of flapping hydrofoil outperforms the PH and RS-types due to relatively high forces as well as the good synchronization of the forces and moment with the translational velocity and pitch angular rate, respectively upon the different aspects of the vortex development. Consequently, the power extraction performance improves from the LS to the PH and then to the RS-types. It is also recognized from another isocontour parametric map that the maximum power extraction efficiency is achieved at a similar maximum effective angle of attack, at the maximum effective angle of attack rate, and at the maximum pitch angle rate for the LS and RS types, while the range of the maximum effective angle of attack rate is lower in the PH-type hydrofoil. (C) 2018 Elsevier Ltd. All rights reserved.