We discovered in Chap. 3 that a special class of solutions, called universal, allows one to determine values of stress by satisfying the equations of equilibrium without knowledge of constitutive relations for solid-like behaviors. There are, however, very few such solutions, thus emphasizing the general need for appropriate descriptions of material behavior under conditions of interest. We learned further in Chaps. 3 , 4 , and 5 that assumptions of linearly elastic material behavior under small strains and rotations admit solutions of stress and strain in diverse types of problems—pressurization of vessels, axial loading of rods, twisting of shafts, bending of beams, and buckling of columns—that prove useful in understanding physiology, designing and interpreting experiments, or designing medical devices. Nevertheless, most cells and soft tissues in the body exhibit nonlinear material behaviors under large deformations and thus require a fully nonlinear analysis. Because the general equations of mass balance and linear momentum balance hold for all continuous media, they are applicable to both linear and nonlinear material behaviors. Experience has revealed that the best approach to studying nonlinear solid mechanics is to start with large strain descriptions of motion.