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.