Abstract Vortex shedding flow of an oscillating vertical cylinder with a disk attached at its keel is considered. This configuration is of interest for the offshore oil and gas industry. A finite difference method is employed to solve the incompressible Navier–Stokes equations in the primitive-variables formulation. Test cases were used to guide selection of the size of flow domain, numerical parameters, and to verify that the resultant method was both convergent and accurate. Numerical simulations have shown that the geometry configurations of the cylinder and disk, such as aspect ratio of the disk t d / D d and diameter ratio, D d / D c have significant influence on the vortex shedding modes and associated hydrodynamic properties, e.g. hydrodynamic damping and added mass coefficients. These in turn affect the performance in heave motion control of the structures.