In　this　paper,　vibration　band　gap　properties　of　periodic　Mindlin　plate　structure　with　two　simply　supported　opposite　edges　are　studied　using　the　spectral　element　method　(SEM).　Based　on　the　Mindlin　plate　theory　(MPT),　the　spectral　Mindlin　plate　stiffness　matrix　is　deduced.　The　spectral　equation　of　the　whole　periodic　structure　is　further　established.　Frequency　responses　are　calculated　by　the　spectral　equations　to　illustrate　band　gap　properties.　Compared　with　the　results　based　on　the　classic　plate　theory　(CPT),　the　effects　of　the　shear　and　rotary　inertia　on　the　band　gap　properties　are　analyzed.　The　results　are　also　compared　with　those　calculated　by　the　finite　element　method　(FEM).　It　can　be　observed　that　the　SEM　is　more　accurate　in　high　frequency　ranges.　Furthermore,　the　influences　of　the　material　properties　and　structure　dimension　on　the　band　gap　behaviors　are　investigated.