Many methods for calculating the hydrodynamic forces on a rigid body, produced by its harmonic oscillations on a free surface have been presented since the analytically method was published by Ursell. Recently, these kind of hydrodynamic problems have been studied using the finite element method (F. E. M.). It seems that F. E. M. can be available to solve the hydrodynamic problems which have been difficult to be solved by other traditional methods becauce of the bodies' complex geometries and their complex boundary conditions. In this papers, as examples of the application of F. E. M. to these kind of hydrodynamic problems, the authors have calculated the added masses and damping coefficients for two-dimensional bodies and also for axi-symmetrical bodies. In order to examine the applicability of F. E. M., the numerical solutions by this method were compared with the solutions obtained by other analyical method, and a good agreement was obtained. As a conclusion, it was found that the finite element technique was a sufficiently accurate and reliable method to solve the hydrodynamic problems of this category.