For the control of vibration and noise of metal structures having relatively low damping, viscoelastic materials are widely used and usually attached at metal structures with an additional constraining layer to secure them. The damping and elastic properties of structures having constrained viscoelastic material layers are dependent on not only temperature and frequency but also their thicknesses. Hence, optimal design of the thicknesses of viscoelastic and constraining layers for a certain base structure are very important to maximize their efficiency and to lighten their weight. In this study, the variation of loss factor of beams having a constrained viscoelastic layer according to the change of thickness has been carefully investigated. From these, optimal design method of the minimum thickness beam having a given loss factor is suggested and numerically verified for a real beam.