A brilliant development of the theory of waves generated by a body oscillating in the free surface has remarkably improved theoretical prediction of ship motion in waves. However, there is yet room for improvement of the accuracy of predicting the rolling motion, because the damping coefficient for rolling is still estimated by a semi-empirical formula. This paper is devoted to improving the estimation of roll-damping force for real ships with usual hull-forms. By the way, Yuasa et al. investigated the hydrodynamic forces acting on an oscillating flat plate immersed enoughly in the fluid in both cases where the flat plate has forward speed and not. On the contrary, this paper deals with the hydrodynamic normal forces to the surface of bilge keel, which damps the rolling motion of a ship. However, for bilge keels attached to three-dimensional bodies, some effects which need not be considered for an oscillating flat plate should be taken into consideration. Among such effects, the effect of mirror image of a bilge keel with respect to the hull surface and the effect of increase of relative flow speed at the bilge are especially important. By taking account of both effects, the authors succeed in relating the damping force acting on the bilge keel without forward speed to that on an oscillating flat plate, and also estimating approximately the damping force of the bilge keel with forward speed by low aspect ratio wing theory for uniform motion.