This chapter explores the constitutive equations that link the deformation and stress fields in soft solids, providing a three-dimensional generalization of Hooke’s law. We introduce the principle of work, demonstrating how the work done during deformation equates to changes in elastic potential (stored) energy. We discuss the concept of objectivity and its implications in terms of the stored energy density. We also examine material symmetry and isotropy, and see how stored energy functions must comply with physical requirements. We then derive stress-deformation relations in terms of strain invariants and in terms of principal stretches. The chapter concludes with examples of useful and popular stored energy functions, including the neo-Hookean, Mooney-Rivlin, Gent, Fung, and Ogden models, highlighting their applications in modelling the behaviour of rubber-like materials and biological tissues.