The　size-dependent　nonlinear　vibration　model　of　the　magneto-electro-elastic　(MEE)　sandwich　nanobeam　on　Winkler-Pasternak　foundation　is　built　based　on　nonlocal　elasticity　theory　and　Reddy＇s　third-order　shear　deformation　theory.　Employing　the　Hamilton　variational　principle　and　von　Karman＇s　geometrically　nonlinear　theory,　the　nonlinear　governing　equation　system　of　MEE　sandwich　nanobeam　is　deduced.　The　expressions　of　nonlinear　frequency　ratio　and　critical　external　electric　and　magnetic　potential　are　derived　with　the　perturbation　method.　Several　cases　are　studied　in　order　to　show　the　influence　of　nonlocal　parameter,　Winkler　and　Pasternak　elastic　foundation,　stacking　sequence,　external　electric　and　magnetic　potential　on　size-dependent　nonlinear　vibration　behaviors　of　MEE　simply　supported　sandwich　nanobeam.