This paper describes a plane regular wave interaction with a combined cylinder which consists of a solid inner column and a coaxial perforated outer cylinder. The outer perforated surface is a thin porous cylinder with an annular gap between it and the inner cylinder. The non-linear boundary condition at the perforated wall is a prime focus in the study;energy dissipation at the perforated wall occurs through the resistance to the fluid across the perforated wall. Explicit analytical formulae are presented to calculate the wave run-up on the outer and inner surfaces of the perforated cylinderand the surface of the inner column. The theoretical results of the wave run-up are compared with previous experimental data. Numerical results have also been obtained: when the ratio of the annular gap between the two cylinders to incidentwavelength (b-a)/L≤0.1, the wave run-up on the inner surface of the perforated cylinder and the surface of inner column can partially or completely exceed the incident wave height.