In　this　paper,　the　band　gap　properties　of　the　periodic　structures　of　bar　system,　which　include　the　rod-joint,　truss,　and　frame　structures,　are　studied　using　spectral　element　method　(SEM).　The　spectral　equations　of　the　rod,　beam,　and　joint　elements　are　established　and　the　spectral　equations　of　the　whole　structures　are　further　assembled.　The　frequency　responses　of　the　whole　structures　are　calculated　and　the　results　are　compared　with　those　calculated　by　the　finite　element　method　(FEM).　It　can　be　observed　that　the　SEM　is　more　accurate　in　high　frequency　ranges.　The　band　gap　properties　of　the　three　types　of　periodic　structures　are　studied,　respectively.　Furthermore,　the　effects　of　structural　length,　unit　cell　number,　structural　configurations,　load　conditions,　and　structural　damping　on　the　band　gap　properties　are　investigated.