As noted in Chap. 1 , in the literature there are some constitutive inequalities that allow the selection of material models with desired properties and/or the establishment of constraints on the parameters included in the constitutive relations for the material models considered. In this book, we test neo-Hookean material models for satisfaction of the constitutive inequalities due to the Hill postulate and the corotational stability postulate (CSP), which extend the constitutive inequality due to Drucker’s postulate from infinitesimal to finite strains. Formulations of these inequalities are given in Sect. 5.1, and testing material models for satisfaction of the Hill and CSP postulates is performed in Sects. 5.3 and 5.4, respectively.