Most　hydrogels　exhibit　coupled　chemo-mechanical　behaviors　when　in　an　aqueous　environment　with　changing　salt　concentrations.　This　work　presents　a　theoretical　framework　and　a　numerical　procedure　to　describe　the　coupled　mechanical　deformation　and　solvent　diffusion　of　such　ion-sensitive　hydrogels.　A　new　variational　formulation　for　the　coupled　governing　equations　is　formulated　by　implementing　the　coupled　formulations　in　a　finite　element　procedure　in　Eulerian　frame　and　further　the　time-dependent　concurrent　process　of　mechanical　deformation　and　solvent　diffusion　is　numerically　investigated.　The　proposed　numerical　method　is　demonstrated　by　analyzing　several　chemo-mechanical　coupling　phenomena　of　initially-swollen　hydrogels,　such　as　transient　free-swelling　and　indentation　with　a　spherical　punch.　The　results　show　that　the　present　model　is　capable　of　simulating　transient　free-swelling　and　solvent　migration　in　such　smart　materials　subjected　to　externally-applied　mechanical　forces.