In　the　current　work,　an　accurate　modified　couple　stress-based　cylindrical　micro-panel　model　is　developed　in　the　framework　of　sinusoidal　shear　deformation　theory.　The　classical　strain　tensors　and　curvature　tensor　components　in　a　modified　couple　stress-based　model　are　given　with　consideration　of　the　geometric　curve　of　cylindrical　panels.　In　conjunction　with　a　general　Lagrange　procedure,　the　proposed　model　is　implemented　to　derive　a　system　of　Mathieu-Hill　equations　of　governing　dynamic　stability　behaviors　of　the　cylindrical　micro-panels.　The　Navier-type　solution　and　Bolotin＇s　method　are　applied　to　predict　the　principle　unstable　regions　of　the　micro-panels　with　simply-supported　boundary　condition.　As　an　application　of　the　proposed　model,　the　size-dependent　stability　of　a　functionally　graded　graphene　nanoplatelets　reinforced　composite　(FG-GNPRC)　cylindrical　micro-panel　under　axial　oscillation　compression　is　investigated　for　the　first　time.　It　is　assumed　that　the　weight　fraction　of　graphene　nanoplatelets　(GNPs)　is　graded　in　the　panel　thickness.　The　effective　Young＇s　modulus　of　FG-GNPRC　is　determined　based　on　a　modified　Halpin-Tsai　model,　while　the　mixture　rule　used　to　evaluate　the　effective　Poisson＇s　ratio　and　the　mass　density.　The　parameter　studies　are　performed　to　examine　the　effect　of　dimensionless　length　parameter,　GPL　distribution　patterns,　GPL　size　and　shape,　length-to-span　ratio　and　radius-to-span　ratio　on　the　sizedependent　dynamic　stabilities　of　FG-GNPRC　cylindrical　micro-panels.