In　this　paper,　based　on　a　diffusion　and　mechanical　coupled　continuum　model,　the　two-dimensional　chemo-mechanical　coupled　problem　in　the　polar　coordinates　is　studied　under　plane　strain　assumption.　The　transient　analytical　expressions　for　concentration　and　stresses　are　obtained　using　a　displacement　potential　function　and　Airy　stress　function.　An　axisymmetric　problem　is　considered　to　verify　the　correctness　of　these　expressions.　After　that,　a　numerical　example　of　a　long　enough　and　traction-free　cylinder　with　variant　concentration　distribution　on　its　cylindrical　surface　by　an　angle　is　given,　and　the　results　show　that　the　shear　stress　on　the　cross　section　is　generated　during　the　process　of　diffusion　and　the　axial　stress　increased　with　the　increment　of　concentration.　The　in-plane　stress　for　this　traction-free　cylinder　will　vanish　at　a　steady-state　when　the　concentration　was　linearly　distributed.　©　2021　by　ASME.