Employing the methods of separation of variables and matched eigenfunction expansions for velocity potential, analytical solutions are proposed for a water wave radiation problem of a floating semi-porous compound cylinder in finite ocean depth. The configuration of the semi-porous compound cylinder is such that it consists of an impermeable inner cylinder rising above the free surface and a coaxial truncated porous cylinder around the lower part of the inner cylinder with the top of the porous cylinder being impermeable. The condition on the porous boundary is defined by applying Darcy's law as in Williams et al. (Ocean Eng 27:1-28, 2000). The translational motions in the x-and z-directions, i.e., surge and heave motions, are investigated. A mathematical model is developed which can be considered as an extension of a number of the earlier works, e.g.,