When a solid body is subjected to external forces, it inevitably undergoes changes in both shape and volume. The response of a body to these forces is inherently dependent on its specific material properties. The objective of this chapter is to describe these material responses through a formulation that links the stress tensor and the strain tensor, known as the constitutive law. This relationship is crucial for understanding the behavior of materials under various loading conditions. To address the growing applications of advanced composite materials and other novel materials, this chapter incorporates a range of constitutive laws, including the anisotropic Hooke’s laws, the elastic constitutive relation for infinitesimal strain with large rotations, and the constitutive laws for hyperelastic materials, in addition to the traditional isotropic Hooke’s law. The isotropic Hooke’s law is introduced through the conceptualization of hypothetical mechanical experiments, providing a clear and accessible foundation. This approach paves the way for the introduction and exploration of the anisotropic Hooke’s laws. The constitutive laws of hyperelasticity are then deduced using the strain energy density function, a method that is also discussed in the context of the isotropic Hooke’s law.