This book introduces new chapters that delve into the structure of electromagnetic and elastic fields in anisotropic media, the detailed solutions of the conductivity and elasticity problems for spherical radially transverse isotropic inclusions, the analysis of the neutral inclusion problem in static conductivity and elasticity, and the homogenization problem for polycrystalline materials. In the second edition of this book, readers will find a comprehensive update on the application of self-consistent methods in material science, reflecting the advancements in computational capabilities since its first publication. It also emphasizes the growing importance of numerical methods, which have expanded the applicability of self-consistent methods, and includes updated references to the latest research in the field since 2008.