A thermodynamic theory under nonhydrostatic stresses is developed to discuss the role of thermodynamic functions in chemical processes, based on the treatment of elasticity involving finite deformation. This treatment makes it possible to examine the attempts made by many investigators to define the chemical potential as a function of the state alone. It is shown that these treatments were not quite rigorous because relative stability depends not only on the state, but also on the process. The chemical potential introduced by the ‘local equilibrium’ theory developed by J. W. Gibbs, W. B. Kamb, and A. G. McLellan is shown to be valid under certain restrictions. An expression of the chemical potential applicable to the case under a small nonhydrostatic stress superimposed on a finite hydrostatic pressure is derived. The states are classified as ‘simple’ or ‘complex’ state, when the bulk stability is treated on the basis of this chemical potential. Application of the theory to crystallographic phase transformation explains the spreading of transition pressure resulting from nonhydrostatic components of stress. Preferred orientations of cubic, hexagonal, and trigonal crystals are discussed, and the result expected from the theory seems to be consistent with the experiments or observations for LaAlO3, α quartz, and ice.