Abstarct: Optimization is used in a wide spectrum of industries, including aerospace, automotive, chemical, electrical and manufacturing industries. In Structural and Mechanical Engineering, optimization is important to design and produce structures both economically and efficiently. This thesis addresses "Topology optimization of 2D problems by using Boundary Variation Method". One of the research traits, is modeling the structure by NURBS because of its power and flexibility in producing various curves and surfaces. The curves were produced using a FORTRAN code made by the author specifically for this study. The control points of inner and outer boundaries are also selected as the design variables. After modeling, Finite element analysis and then optimization process is carried out. During optimization process with changing the position of control points and in turn moving the boundaries, shape and topology optimization of structures are changed. This method has the advantage of different objective functions while the application of displacement and stress constraints are also possible. The results show that, using NURBS technique in structural modeling, decrease the number of design variables and is saving the time and cost. In this method convergence speed is improved and solution accuracy is increased. Finally several examples are presented to show the method efficiency.