A　size-dependent　improved　third　order　shear　deformable　computational　framework　with　the　aid　of　modified　couple　stress　theory　(MCST)　is　developed　to　investigate　the　stability　and　free　vibrations　of　polymer-based　microbeams　reinforced　by　graphene　oxides　(GOs).　The　nanocomposite　microbeams　are　placed　in　an　elastic　substrate　and　have　different　immovable　end　restraints.　The　modulus　of　elasticity　of　the　GOs-reinforced　nanocomposite　(GORC)　is　evaluated　using　the　well-known　Halpin-Tsai　micromechanics　model,　and　the　equivalent　mass　density　as　well　as　Poisson＇s　ratio　is　evaluated　based　on　mixture　rule.　The　equations　governing　the　stability　and　vibration　behaviors　are　derived　by　means　of　the　Lagrange　method　with　the　help　of　the　Gram-Schmidt　process　that　is　used　to　produce　admissible　functions　in　a　general　orthogonal　polynomial　form.　The　static　stability　and　vibration　characteristics　of　the　GORC　microbeams　are　analyzed.　The　influences　of　small-scale　effect,　GO　nanofillers,　and　elastic　foundation　on　the　mechanical　stability　and　vibration　behaviors　of　the　nanocomposite　microbeams　are　illustrated　using　some　numerical　examples.