The　aim　of　present　work　is　to　propose　a　unified　modified　couple　stress-based　shear　deformable　shell　model　that　has　capability　of　analyzing　size-dependent　free　vibrations　of　functionally　graded　(FG)　cylindrical　microshells.　In　the　current　model,　the　classical　strain　tensors　and　curvature　tensor　components　are　given　within　the　framework　of　a　unified　high-order　shear　deformation　theory.　The　trapezoidal　shape　factor　is　taken　into　account　for　achieving　reasonable　stress　resultants　over　thickness　and　makes　the　proposed　model　more　accurate　for　thick　shell　structures.　Various　classical　boundary　conditions　of　the　cylindrical　microshells　are　considered　using　the　admissible　functions　of　the　displacements　containing　a　beam　modal　function.　The　governing　equations　associated　with　free　vibrations　of　microshells　are　derived　using　a　standard　Lagrange　method.　A　few　comparisons　are　conducted　and　verify　that　the　results　from　the　current　model　coincide　favorably　to　the　ones　from　three-dimensional　elasticity　solutions.　The　comparisons　also　prove　that　the　proposed　model　has　a　sufficient　capability　of　dealing　with　free　vibration　problems　of　the　thick　functionally　graded　cylindrical　microshells.　To　the　end,　the　size-dependent　free　vibrations　of　an　FG　cylindrical　microshell　are　investigated.　As　new　results,　natural　frequencies　of　the　FG　microshells　with　various　boundary　conditions　are　tabulated,　and　the　effects　of　some　important　parameters　on　vibration　characteristics　of　FG　microshells　are　discussed.