The　interaction　between　the　core　and　external　restraining　members　of　the　buckling-restrained　brace　(BRB)　should　be　considered　because　of　the　significant　effect　it　may　cause　on　the　overall　performance　of　BRBs.　The　mechanism　of　core　member　multi-wave　deformation　is　studied　for　the　first　time　in　this　research,　which　presents　an　actual　flexural　wave-shape　development　of　core　member　with　increasing　axial　load　and　reveals　the　contact　force　distribution　and　development　between　the　core　and　external　restraining　members　by　employing　the　refined　finite　element　(FE)　analysis.　The　object-oriented　programming　language　Python　is　applied　in　the　ABAQUS　parameter　analysis,　and　the　influences　of　initial　imperfection　of　the　core　and　external　restraining　members,　as　well　as　that　of　the　gap　amplitude,　on　BRB　performance　are　also　investigated.　Numerical　simulation　results　show　that　the　reverse　bending　of　core　member　triggered　sudden　buckling　in　high-order　modes,　as　well　as　the　overall　stress　decrease　in　the　external　restraining　member,　whereas　the　local　stress　increased　with　the　development　of　the　core　deformation　waveform.　The　BRB　with　the　core　of　symmetric　initial　imperfection　performed　worse　than　that　with　the　core　of　anti-symmetric　initial　imperfection　in　compression.　Furthermore,　less　initial　deflection　of　external　restraining　members　and　gap　amplitude　leads　to　smaller　contact　force,　thus　the　BRB　can　perform　more　effectively.