Let us begin by recalling three important observations from Chaps. 1 and 2 . First, equilibrium requires that the sum of all forces must be zero, namely, ΣF = 0, and the sum of all moments must be zero, ΣM = 0. Second, if a body is in equilibrium, then each of its parts are likewise in equilibrium. Third, there may exist at each point p in a body (cf. Fig. 2.4 ) nine components of Cauchy stress, six of which are independent, which we denote as σ(face)(direction) relative to the coordinate system of choice. Although we also generally seek to determine the associated values of strain at each point in the body and to associate the stress and strain at each point to quantify the material behavior via a constitutive relation, here we begin our formal analysis by deriving general equations in terms of stress that must hold at each point in the body to enforce equilibrium. Next, we will find that special solutions, called universal, can be determined in a few cases wherein equilibrium can be satisfied via statics alone, without knowledge of a constitutive relation. Such solutions are useful both experimentally and theoretically. Finally, we conclude this chapter by examining two examples of equilibrium wherein full solutions can only be determined with knowledge of a constitutive relation, which is most often the case.