Many　continuum　media,　often　described　as　multifunctional　materials,　exhibit　multi-field　coupling　behavior　and　are　sensitive　to　external　environmental　stimuli.　Chemo-mechanical　coupling　behavior　for　continuum　media　was　investigated　in　this　paper.　From　the　point　view　of　the　thermodynamics　and　chemical　potential,　we　have　obtained　the　constitutive　equations　and　governing　equations　of　chemo-mechanical　coupling　problem.　Energy　functional　of　chemo-mechanical　coupling　equations　has　been　established　by　variational　principle,　and　then　the　equivalent　integration　forms　and　finite　element　formulation　of　the　coupled　governing　equations　are　derived.　The　chemo-mechanical　coupling　behaviors　of　continuum　media　are　analyzed　by　numerical　examples.　The　numerical　results　show　that　the　mechanical　and　chemical　fields　interact　with　each　other　in　a　medium.　The　deformation　of　media　is　caused　by　the　concentration　variation.　Similarly,　the　external　mechanical　force　can　also　induce　concentration　redistribution.　The　basic　theory　and　simulation　method　can　be　applied　to　analysis　of　chemo-mechanical　coupling　behavior　of　continuum　media.　The　chemo-mechanical　coupling　behavior　of　continuum　media　can　be　reflected　clearly　in　the　present　model.