Abstarct: The purpose of this thesis is to use the boundary variation techniques for structural topology, as well as, shape optimization. The conventional boundary variation methods are not suitable for topology optimization of elastic structures with mean compliance and the volume of the consumable material as the objective function and the constraint respectively. In this approach the moving boundaries of the structure during the optimization process is modeled by the zero level set of an implicit scalar function of a higher dimension. This easily provides us with the appropriate variation of shape and topology of the structure. To verify the applicability and performance of the method an academic program, given the name TOLS (Topology Optimization with Level Set) was developed and a few examples were executed.