The present work investigates the physics of constrained layer damping treatments for plates and beams by a semi-analytical finite element method and presents applications of the method to the optimization of damping treatments. The method uses finite element discretizations in the thickness coordinate and propagating wave solutions in the remaining coordinates and therefore provides more generality and accuracy than existing analytical approximations. The resulting dispersion equation is solved for complex-valued wave numbers at each frequency of interest. By choosing sufficiently fine discretizations in the thickness coordinate, the method gives accurate estimates of wave numbers. The numerical implementation of the method is an efficient yet general tool for optimizing damping treatments with respect to material properties and dimensions. It explicitly allows for the possibility of analyzing structures with several layers where the material of each layer may be isotropic or orthotropic. Examples illustrate the numerical efficiency of the implementation and use this efficiency to provide optimizations of constrained layer damping treatments.