This paper deals with the optimization of wave absorbers oscillating about a fixed submerged horizontal axis. A multiobjective optimization algorithm is employed to search for the optimal geometries where two cost criteria are used as the objective functions to be minimized. The two cost criteria are the ratios, integrated over a specified frequency range, of the submerged surface area to the maximum absorbed power, and of the maximum reaction force to the maximum absorbed power. Geometric configurations with uniform simple cross-sectional shapes, viz. line, circle, and elliptical sections, are considered. For each configuration, the body dimensions and submergence, as well as the submergence of the rotation axis, are the variables to be optimized. It is found that most of the optimal geometries have their rotation axes close to the sea bottom and their bodies close to the free surface. The optimal size of the geometries varies depending on the selected wave frequency range, but the optimal cross-sectional dimensions are generally less than one third of the water depth when optimized over a uniform distribution of wave frequencies from 0.4 to 1.3 rad/s. Among the cross sections considered, the elliptical one performs best.