The mesh-free radial basis function(RBF) collocation method is explored to calculate band structures of periodic composite structures. The inverse multi-quadric(MQ), Gaussian, and MQ RBFs are used to test the stability of the RBF collocation method in periodic structures. Much useful information is obtained. Due to the merits of the RBF collocation method, the general form in this paper can easily be applied in the high dimensional problems analysis. The stability is fully discussed with different RBFs.The choice of the shape parameter and the effects of the knot number are presented. The mesh-free radial basis function (RBF) collocation method is explored to calculate band structures of periodic composite structures. The inverse multi-quadric (MQ), Gaussian, and MQ RBFs are used to test the stability of the RBF collocation method in periodic Structures. Much useful information is obtained. Due to the merits of the RBF collocation method, the general form in this paper can easily be applied in the high dimensional problems analysis. The stability is fully discussed with different RBFs.The choice of the shape parameter and the effects of the knot number are presented.