Abstarct: Topology optimization is one of the most important kinds of structural optimization problems, aims to find the optimum distribution of materials in a certain domain. To reach the point, different objective functions and constraints might be considered. During the last decade, two general approaches on topology optimization problems have been developed. In more common approach, the compliance or energy of deformation is minimized for a given amount of materials. The other approach is to minimize the weight of structures under stress or displacement constraints. The main goal of this research is to utilize the Isogeometric Analysis (IA) method in topology optimization problems with minimum weight approach. In addition, the IA formoulation for materially nonlinear structures is derived baxsed on Elasto-Plastic materials. The effect of considering nonlinear analysis on topology optimization problems is also studied. The Method of Moving Asymptotes (MMA) is employed for optimization process in which derivatives of the objective function and constraints with respect to the design varibales (sensitivity analysis) are needed to be determined. In this thesis, first the IA formulation of plane stress structures considering elasto-plastic materials is explained. Then, the topology optimization problem with minimum weight approach subject to stress constraints for elastic materials is formulated when IA is used. To achieve this and in order to demonstrate the effect of elasto-plastic deformations on optimum topology of structures, fortran codes for isogeometric topology optimization of elastic and elasto-plastic structures are developed. Finally, the outputs are verified through several numerical examples.