Abstarct: The primary objective of this thesis is the topology optimization of plane stress problems with a focus on maximizing ductility under a material volume constraint. Given that the optimal design of structures cannot adequately address real-world performance conditions by solely considering linear material behavior, it is essential to incorporate nonlinear material behavior into the optimization process. This approach enables the development of designs with greater reliability in practical applications. Therefore, this thesis emphasizes the influence of nonlinear material behavior on the topology optimization process to offer a more practical solution for structural design. To solve the problem, the Solid Isotropic Material with Penalization (SIMP) method, combined with the Method of Moving Asymptotes (MMA) optimization algorithm, is employed. This combination ensures an efficient and stable solution of the optimization problem. Furthermore, the Finite Difference Method is used to compute the derivatives of the objective function with respect to the design variables, achieving the desired accuracy in the topology optimization process. The chosen approach in this thesis is baxsed on striking a balance between computational precision and algorithmic efficiency, enabling effective performance across various structural analysis conditions.The main innovation of this thesis lies in integrating two distinct computational environments: the topology optimization algorithm is developed in Python, while the finite element analysis is conducted using the powerful software Abaqus. This integration leverages the flexibility of programming and the high capability of numerical analysis simultaneously. Through this approach, ductility maximization in plane stress structures is achieved innovatively and accurately. The results demonstrate that considering nonlinear material behavior leads to a more optimal design compared to the linear case. Thus, this thesis represents a step toward developing practical and reliable tools in the field of structural optimization.