This book provides a comprehensive and practical introduction to the Boundary Element Method (BEM) as applied to the analysis of plates, shells, and thin-walled structures in solid mechanics. Addressing a significant gap in the existing literature, the book offers a detailed and accessible exploration of BEM, covering a wide range of engineering problems including static, dynamic, fracture, buckling and nonlinear analysis. It combines theoretical foundations with practical applications, making complex concepts approachable for final-year students, graduate students, and practicing engineers. The book also introduces open-source computational tools, allowing readers to implement and apply BEM theories in real-world engineering scenarios, a resource scarcely available in current literature. By covering both classical and advanced topics in plate and shell theory, including the analysis of isotropic and laminated composites, the book serves as a vital guide for anyone looking to deepen their understanding of BEM in solid mechanics, with a clear focus on its practical application in engineering.