A two-dimensional (2D) panel method is developed to find the first and second order wave forces acting on a semi-submerged cylinder in regular waves. The panel method is based on potential flow and the waves are modeled for both finite and infinite water depth. The motion is limited to heave, but allows for extensions to other modes as well. It uses boundary conditions for floating body dynamics with Neumann and mixed type boundaries on the surfaces. The waves are generated and the reflection of the waves is suppressed by generating absorbing boundary conditions (GABC) on the radiation surfaces. The model is used to investigate the hydrodynamics of an oscillating buoy wave energy converter (point energy converter). For this, an analytical solution of the optimal damping is used. The method uses panels along all boundaries to solve the boundary conditions. The model can be used for any time-harmonic free surface flow problem. A second order wave running through the domain is successfully modeled, without the interference of a body. Challenges of a second order model with body are explained. The boundary element method has innate challenges finding the correct solution to tangential flows on the panels and spatial derivatives of the velocity, which are required for the second order solutions.