In this paper, the finite element technique incorporating the infinite element is applied to the evaluation of hydrodynamic forces on offshore structures. The hydrodynamic forces are assumed to be inertially dominated, and the viscous effects are neglected. Two types of elements are developed to discretize the fluid domain efficiently. They are the infinite elements developed to model the radiation condition at infinity, and the fictitious bottom boundary elements introduced to avoid extensive fluid domain discretizations for the case of deep water. The shape functions of the infinite elements, in the radial direction, are derived from the asymptotic expressions for the progressive wave and the first evanescent mode components in the analytical boundary series solutions. Numerical analyses are performed for vertical axisymmetric bodies to validate the infinite elements and the fictitious bottom boundary elements developed in this study. Comparisons with the results from other available numerical solution methods show that the present method gives fairly good results. Numerical experiments are also carried out to determine the proper distance to the infinite elements and the fictitious bottom boundary elements from the solid body, which directly affect accuracy and efficiency of the solution.