In many real-world applications, solid objects subjected to mechanical loads often exist in environments where physical quantities beyond mechanics—such as temperature, mass concentration, and electrical fields—can deviate from their initial states. To address these complex interactions, this chapter examines how these non-mechanical factors influence mechanical deformation and stress in elastic solids. We formulate constitutive equations that incorporate multi-physics phenomena, treating strains induced by various non-mechanical quantities (in the absence of mechanical stress) as eigenstrains, regardless of their physical origins. Within a one-way coupling framework, we develop methodologies for solving multi-physics boundary value problems. These methods provide a systematic approach to understanding how non-mechanical factors affect the mechanical behavior of materials. Additionally, the chapter includes a brief introduction to two-way coupling problems, where mechanical and non-mechanical fields influence each other, highlighting the complexity and importance of such interactions in advanced engineering applications.