This paper presents a generalization of a computational method for the linearized potential flow, previously applied to a two-step vertical cylinder. Equations for the study of hydrodynamic forces on a cylinder with a large number of steps are given. This procedure is applied to a compound cylinder with three radii, in heave motion, as an example. Experimental results for heave motion are compared to the numerical ones. Added mass and damping coefficients and the exciting forces for different cylinders are reported.