Frequencies　and　energies　of　vibrations　for　a　honeycomb　sandwich　plate　with　negative　Possion＇s　ratio　are　investigated.　Based　on　Reddy＇s　third-order　shear　deformation　plate　theory,　von　Karman　type　nonlinear　theory　and　Hamilton　theory,　the　equations　of　motion　for　the　plate　are　obtained,　free　vibrations　and　vibrations　with　the　damping　and　in-plane　force　of　the　plate　are　considered,　respectively.　The　changes　of　real　parts　of　the　eigenvalues　with　the　damping　and　in-plane　forces　of　the　plate　are　obtained.　In　order　to　obtain　the　analytic　solutions　of　the　frequencies　and　energies　of　the　plate,　lateral　free　vibrations　are　considered　by　using　the　Hamilton　energy　method,　and　we　compare　the　results　with　that　of　the　previous　free　vibrations.　The　potential　energies　and　the　total　energies　variation　with　parameters　of　the　plate　are　given.　The　research　results　from　the　two　methods　show　that　the　change　trends　of　the　frequencies　and　energy　of　the　plate　are　exactly　consistent,　but　the　values　of　natural　frequencies　and　potential　energies　are　lager　in　lateral　vibrations.