The Saint-Venant’s problem for anisotropic elastic bodies has been extensively studied [28,175,204,313]. We note that the researches devoted to SaintVenant’s problem are based on various assumptions regarding the structure of the prevailing fields of displacement or stress. It is the purpose of this chapter to extend the results derived in the previous chapters to the case of anisotropic elastic bodies with general elasticities. The procedure presented in this chapter avoids the semi-inverse method and permits a treatment of the problem even for nonhomogeneous bodies, where the elasticity tensor is independent of the axial coordinate. Saint-Venant’s problem for nonhomogeneous elastic cylinders where the elastic coefficients are independent of the axial coordinate has been studied in various works [150,152,318]. According to Toupin [329], the proof of Saint-Venant’s principle presented in Section 1.10 also remains valid for this kind of nonhomogeneous elastic bodies.