The　in-plane　vibration　problem　of　functionally　graded　(FG)　sandwich　circular　arch　made　up　of　two　layers　of　power　law　FGM　face　sheet　and　one　layer　of　homogeneous　core　is　investigated.　A　framework　for　the　vibration　analysis　of　FG　sandwich　circular　arches　is　presented,　and　the　quasi-3D　theories　for　the　arch　structures　compatible　with　this　framework　are　established　for　the　first　time.　The　quasi-3D　theories　take　into　account　the　changes　of　displacement　through　the　thickness　of　the　arch,　and　satisfy　the　stress-free　boundary　conditions　naturally.　The　Lagrange　equation　is　employed　to　derive　the　equation　of　motion,　and　various　boundary　conditions　are　implemented　by　applying　simple　algebraic　polynomials　as　admissible　functions　to　discrete　the　displacement　fields　of　the　FG　sandwich　arches.　The　comparison　study　of　various　high-order　shear　deformation　theories　and　quasi-3D　deformation　theories　for　the　FG　sandwich　circular　arches　is　carried　out　via　different　numerical　examples.　The　influences　of　material　distributions　and　geometric　parameters　on　the　vibration　characteristics　of　the　FG　sandwich　circular　arches　are　also　presented　and　discussed　for　the　first　time.