Bi-stable structures are characterized by the ability to maintain two distinct configurations, even in the absence of external loads. This dual stability can be achieved through either material manipulation or geometric design, with this thesis placing particular emphasis on the latter approach. This thesis explores the design and analysis of bi-stable structures constructed from composite materials, with a focus on the geometric approach to achieving bi-stability. By investigating the relationship between geometric parameters—such as length, length-to-height ratios, and thickness of composite sections—and their influence on stability, this research advances our understanding of these versatile structures. Beginning with the analysis of single arch structures and progressing to the study of cell formations composed of two arches, and finally to entire meta structures made of these cells, this study systematically examines the behavior and stability of bi-stable configurations. A key insight of this investigation is the significant impact of external boundaries on the stability of composite bi-stable structures. However, controlling these boundaries poses challenges, especially when dealing with deformations within a meta structure adjacent to multiple cells. To address this challenge, innovative strategies for achieving localized deformations within the meta structure are proposed and discussed. Through rigorous finite element analysis, this thesis not only contributes to the fundamental understanding of bi-stable structures made of composite materials but also offers practical insights into their design and implementation in real-world applications. The findings presented here pave the way for the development of innovative and adaptable bi-stable structures with enhanced performance and functionality, opening new avenues for exploration in structural design and engineering. Furthermore, it is worth noting that these bi-stable structures hold significant potential for application in space exploration, particularly as deployable structures. Their inherent ability to maintain stable configurations without continuous external support makes them ideal candidates for space missions where compactness during transportation and reliable deployment are essential. The versatility and adaptability of these structures make them promising assets for future space endeavors, enhancing the efficiency and effectiveness of space exploration missions.