Spar platforms with cylindrical shape and constant cross-section area may experience resonant heave motions in sea states with long peak periods, which are probably excessive for riser integrity due to its low damping and relatively low natural heave period. Changes to hull shape and cross-section that produce more benign heave behavior were discussed by some researchers in the past. In this study, the viscous damping of spar structures is explicitly calculated, and incorporated to the potential solution. It is concluded that the heave resonant response can be considerably reduced by alternative hull shapes via increased damping mechanism and the natural heave period being kept outside the range of the wave energy.