Based　on　the　generalized　moving　least　square　method,　a　new　Element-Free　Galerkin　(EFG)　double-variable　approximation　is　applied　to　dynamic　characteristic　calculation　and　analysis　of　Euler　beam.　In　the　development　of　the　approximation,　displacement　boundary　conditions　are　imposed　with　penalty　method,　and　mass　matrix　and　stiffness　matrix　are　created　catering　for　the　implementation　of　EFG.　Natural　frequencies　and　natural　modes　of　four　Euler　beams　with　different　boundary　conditions　are　calculated　by　double-variable　EFG.　Comparing　the　proposed　approximation　with　theoretical　solution,　finite　element　method　(FEM)　and　single-variable　EFG,　it　is　concluded　that　the　proposed　approximation　has　higher　interpolation　precision　and　applicable　to　complicated　boundary　conditions.　Especially,　it　is　more　accurate　than　FEM　in　higher　modes.　With　trial　method,　the　order　of　polynomial　is　discussed　and　then　its　reasonable　value　is　given.