Generalized　moving　least　square　method　is　the　theoretical　basis　of　a　new　Element-Free　Galerkin　(EFG)　double-variable　approximation.　Deflection　and　angle　of　rotation　are　both　considered　in　the　new　method.　Mass　matrix　and　stiffness　matrix　of　Euler　beam　are　established　with　EFG　and　free　vibration　is　analyzed.　Dynamic　characteristics　of　three　Euler　beams　with　different　boundary　conditions　are　calculated.　It　indicated　that　double-variable　approximation　has　smaller　interpolation　error　than　single-variable　approximation,　and　it　is　more　accurate　than　FEM　of　higher-order　modes.　With　trial　method,　scale　of　influence　radius　is　discussed　and　then　3.5　is　regarded　as　its　reasonable　values.　Based　on　Euler　beam,　free　vibration　of　girder　system　is　calculated　with　EFG　and　the　accuracy　in　complex　model　is　shown.