Abstract: The mechanism and constitutive equation about mechanical properties of materials is one of the important factors in materials science research. Although many works have been done in these aspects, unfortunately, up to now, it is difficult to guide qualitatively and quantitatively the exploitation, processing and development of materials in theory. This paper proposes the thermodynamic micromechanism of mechanical properties for crystal materials, and deduces and obtains some important relationship equations about the mechanics properties of crystal materials. In this part, furthermore, the elasticity and its constitutive relationship for metallic single crystal materials are concretely researched. The results and data are well close to the practical phenomena and the experimental results.