The nonequilibrium thermodynamics of polycrystalline solids under nonhydrostatic stress are formulated, based on the conservation laws of classical dynamics and the second law of thermodynamics. For a closed system, the thermodynamic potential function corresponding to the Gibbs free energy, in classical thermodynamics, is defined as a Legendre transformation of the internal energy of the system, whereas it cannot be defined in an open system under stress. Chemical potential is defined at source points where addition of matter is possible. Chemical potential for grain growth (μ+) under nonhydrostatic stress varies with the orientation of grain surfaces and with direction of grain growth. Pressure solution, diffusion creep, and anisotropic phase equilibrium under stress are explained by the orientation dependence of μ+. ¿ American Geophysical Union 1992