In　this　paper,　the　vibration　band　gap　properties　of　a　two-dimensional　square　lattice　are　studied　using　the　spectral　element　method.　Before　assembling　the　spectral　equations　of　whole　structures,　the　spectral　stiffness　matrices　of　the　tensional　and　bending　elements　are　established.　The　frequency　responses　of　the　lattices　are　calculated　and　compared　with　those　obtained　by　the　finite　element　method.　It　can　be　observed　that　the　results　in　the　spectral　element　method　are　more　accurate,　especially　in　high　frequency　ranges.　The　frequency　band　gap　properties　are　analyzed　based　on　the　accurate　frequency　responses.　The　effects　of　the　material　and　structure　parameters　on　the　band　gap　properties　are　investigated.