Abstract: Based on definition of chemical potential, and the first law and the second law of thermodynamics, the basic equations of chemo-mechanical coupling problem are investigated in the present paper. The constitutive equations are established by using Helmholtz free energy and then the governing equations are obtained by applying integration by parts to energy functional. It is indicated that the chemo-mechanical coupling system is closed. To build the finite element formulations of the coupling problem, an equivalent integration form of the governing equations is derived from the weighted residual method. This investigation can contribute to understanding the coupling mechanism of chemical and mechanical behavior.