In this paper a discrete-vortex-method(DVM) is presented for investigating the hydromechanics of the planar hydrofoils performing the undulatory motion which can be related to fish propulsion with carangiform mode. This is an extention of the authors previous work(1981) on the 2-dimensional hydrofoil. The applicability and accuracy of the present method are shown by means of comparing the calculated lifts and moments, and their distributions over the planforms with those in available references, for aspect ratio 1.0 and 2.0 rectangular hydrofoils and a swept-back hydrofoil of aspect ratio 2.0 from reduced frequency 0.1 to 0.5. The agreement is considered good. To assure the applicability of the DVM to the study of the propulsive performance of the oscillating planar hydrofoils, the convergence tests are performed. The mean thrust(in pure heave, this is wholly due to leading-edge suction), the mean power to maintain the motion and the hydromechanical efficiency are calculated for the rectangular hydrofoil of aspect ratio 8.0 and these are compared with the calculations by Chopra & Kambe(1977) and Lan(1979) for the same cases.