Laminating　a　thin　layer　of　elastomeric　grating　on　the　surface　of　a　prestretched　dielectric　elastomer　(DE)　membrane　forms　a　basic　design　of　electrically　tunable　transmission　grating.　We　analyze　the　inhomogeneous　deformation　of　a　circular　multiple-region　configuration.　Variation　of　the　geometric　and　material　parameters,　as　well　as　of　the　critical　condition　determined　by　loss　of　tension　instability,　is　probed　to　aid　the　design　of　a　DE-based　deformable　grating.　The　predicted　changes　in　the　grating　period　agree　substantially　with　the　experimental　results　reported　by　Aschwanden　et　al　(Aschwanden　et　al　2007　IEEE　Photon.　Technol.　Lett.　19　1090).