Shape optimal design of two-dimensional elastic components is formulated using boundary elements. The design objective is to minimize compliance of the structure, subject to an area constraint. All degrees of freedom of the model are at the boundary and there is no need for calculating displacements and stresses in the domain. Formulations based on linear and quadratic boundary elements are developed. The corresponding nonlinear programing problem is solved by Pshenichny’s linearization method. The model is applied to shape optimal design of several elastic structural components. The advantages and disadvantages of the boundary element method over the finite element technique for shape optimal design of structures are discussed, with reference to applications.