The　transverse　vibrations　and　stability　of　an　axially　moving　sandwich　beam　are　studied　in　this　investigation.　The　face　layers　are　assumed　to　be　in　the　membrane　state,　which　bears　only　axial　loading　but　no　bending.　Only　shear　deformation　is　considered　for　the　soft　core　layer.　The　governing　partial　equation　is　derived　using　Newton＇s　second　law　and　then　transferred　into　a　dimensionless　form.　The　Galerkin　method　and　the　complex　mode　method　are　employed　to　study　the　natural　frequencies.　In　comparison　with　the　classical　homogenous　axially　moving　beam,　the　gyroscopic　matrix　is　no　longer　skew-symmetric　because　of　the　introduction　of　the　soft　core.　The　critical　speed　for　the　divergence　of　the　axially　moving　sandwich　beam　is　analytically　obtained.　The　contribution　of　the　core　layer　shear　modulus　to　the　natural　frequencies　and　critical　speed　is　discussed.