As the main organ of the body, the load-bearing ability of bone is closely connected to its biomechanical properties. Bone is a complex hierarchical biomaterial, whose biomechanical properties are determined by its own structure and biological characteristics. Because of its mechanical adaptability, bone tissues represent different biomechanical properties under different mechanical loading. To quantify the complicated properties of bone and provide an accurate theoretical basis for clinical research, it is necessary to give insight into the biomechanical properties of bone at different levels and the constitutive relationships of bone tissues. In this review, relative researches on constitutive relationships in recent years were summarized based on its hierarchical biomechanical properties.