The hydrodynamics of a freely floating compound cylinder consisting of a surface-piercing cylindrical column resting on a larger, concentric cylindrical base are investigated theoretically. Linear wave theory and small-amplitude structural oscillations are assumed, and an eigenfunction expansion approach is used to obtain semi-analytical expressions for the hydrodynamic excitation and reaction loads on the structure. Numerical results are presented for a range of wave and structural parameters. It is found that for certain parameter combinations, negative surge/sway added mass coefficients are predicted. The numerical results for the hydrodynamic quantities obtained by the eigenfunction approach have been verified with those obtained by the linear radiation/diffraction program UHWAVE. These results have implications for the tow-out analysis of large gravity-base oil production platforms.