We consider wave forces on fixed porous cylinders with and without a solid inner cylinder and wave-induced motions of floating cylinder with and without a porous outer cylinder. Comparisons between experimental measurements and numerical predictions from an iterative boundary element method (BEM) model are presented. The BEM model assumes that pressure drop across porous surface is proportional to the square of the velocity through the surface. It is shown that the BEM model is able to accurately predict the nonlinear variation of the forces with wave amplitude or motion amplitude. It is demonstrated that adding a porous outer cylinder to a solid vertical cylinder leads to increased excitation force on the combined structure. For floating cylinders adding a porous outer cylinder also leads to a corresponding increase in excitation force. However, the porous outer cylinder provides a larger increase in the damping, resulting in reduced motion response. Further numerical simulations indicate that placing the porous cylinder lower in the water column can lead to increased damping without the corresponding increase in excitation forces. It is shown that for low Keulegan Carpenter numbers, the damping coefficient for a porous cylinder is significantly higher than the viscous damping on a solid cylinder. The results suggest that porous materials could be beneficial for motion damping of floating structures.