This dissertation presents a numerical method to optimize the thickness distribution of three-dimensional structures with respect to various vibrational and structural properties. A combination of a commercially available finite element software package and additional user-written programs is used to modify the shape (but not the number of nodes and elements) of finite element models of the structures to be optimized. This is done iteratively and without manual intervention so as to achieve significant improvements of the objective function. The optimization process continues automatically until some predefined convergence criterion is met or until some prespecified maximum number of iterations is reached.