Abstarct: The aim of this research is to investigate the performance of topology optimization algorithms in addressing potential issues in the production of parts using 3D printing technology. 3D printing, or more broadly, additive manufacturing, is one of the new technologies that has made significant changes in the manufacturing industry in recent years. Due to the laxyer-by-laxyer process of material printing, one challenge that has caught designers’ attention is the instability of overhanging surfaces, which may sometimes comprise a significant portion of the part’s geometry. One fundamental solution to this challenge is the use of support structures, which has been examined in numerous studies. Given the necessity of removing these supports after the part is produced, the optimal design and reduction of material consumption in these structures have always been a topic of interest among design engineers. A review of past studies shows that among the various methods proposed to solve this issue, the use of structural optimization algorithms, particularly topology optimization, has found a special place. In this thesis, the topology optimization of support structures is studied, considering the optimization problem for supports aiming to minimize strain energy under volume constraints using the isogeometric analysis method. For this purpose, two different situations from the perspective of geometric modeling are introduced in the thesis, and for each, a density baxsed topology optimization algorithm is proposed. In the first case, the design domain of the supports is easily separated from the main structure using isogeometric patches, while the second case occurs when the main structure itself is optimized using topology optimization, and the supports need to be positioned within the holes. To avoid identifying boundaries and re-meshing processes to separate the design domain of the supports from the main structure in the second case, a parameterization technique is proposed for the automatic identification of the support design domain, and two separate density functions are used to describe the main structure and the support design domain. The example results show that the proposed algorithms are effective for designing support structures.