A preliminary feasibility study is made of the efficiency of tuned vibration absorbers for reducing response of floating bodies, such as offshore platforms, barges, and so on, to random ocean waves. The absorbers are submerged spring-loaded flaps, with stiffnesses of the springs being adjusted for tuning to any specific (rigid-body) mode of the platform (heaving, pitching, etc.), whereas actual design of the flaps should provide the desired amount of drag-induced damping. Mean square response analysis of the system is made for the case of a narrow-band random excitation due to ocean waves by using method of moments in conjunction with statistical linearization (with Gaussian closure) for quadratic damping term. Extensive parametric study is made of the efficiency of vibration control through the use of absorbers, as represented by the root-mean-square (RMS) response reduction factor. In particular, the efficiency increases with the absorber/platform mass ratio, and it may be of some practical importance even at values of this ratio as small as 1%. The importance of the excitation bandwidth is demonstrated. It is shown that, whereas optimal damping of the absorber depends on the level of wave excitation, the RMS response reduction factor is fairly constant within a rather broad range of (nonlinear) damping, so that adjusting absorber damping for storm level may not be necessary.