The semi-analytical method, widely used for calculating derivatives of static response with respect to design variables for structures modeled by finite elements, is studied in this research. The research shows that the method can have serious accuracy problems for shape design variables in structures modeled by beam, plate, truss, frame, and solid elements. Local and global indices are developed to test the accuracy of the semi-analytical method. The local indices provide insight into the problem of large errors for the semi-analytical method. Local error magnification indices are developed for beam and plane truss structures, and several examples showing the severity of the problem are presented. The global index provides us with a general method for checking the accuracy of the semi-analytical method for any type of model. It characterizes the difference in errors between a general finite-difference method and the semi-analytical method. Moreover, a method improving the accuracy of the semi-analytical method (when possible) is provided. Examples are presented showing the use of the global index. / Ph. D.