Free　vibration　of　the　functionally　graded　material　(FGM)　sandwich　doubly-curved　shallow　shells　under　simply　supported　conditions　is　presented.　Three　common　types　of　the　shell,　namely,　the　shell　with　homogeneous　hardcore　and　FGM　facesheet　(type　A),　the　shell　with　homogeneous　softcore　and　FGM　facesheet　(type　B)　and　the　shell　with　FGM　core　and　homogeneous　facesheet　(type　C),　are　discussed.　The　dynamics　model　is　derived　according　to　a　new　shear　deformation　theory　with　stretching　effects.　The　dimensionless　natural　frequency　is　obtained　by　Navier　method.　Numerical　examples　of　the　FGM　sandwich　doubly-curved　shallow　shells　are　provided　for　different　gradient　material　parameters,　core　thicknesses,　radii　of　curvature,　aspect　ratios,　side-to-thickness　ratios　and　vibration　modes　to　demonstrate　the　accuracy　of　the　present　theory.　(C)　2017　Elsevier　Ltd.　All　rights　reserved.