Abstract: A defect state in the non-Bragg band gaps is investigated by introducing a straight tube into a cylindrical waveguide with periodic rectangular boundaries.The non-Bragg defect state,containing the more complex high-order guided wave modes,is quite different from that in the well-known Bragg gaps.The numerical simulation indicates that the frequency of the non-Bragg defect modes relies on the geometric parameters of the introduced defect.It moves to the low frequency region as the length of the introduced tube increases.But when the radius gets larger,the frequency of the non-Bragg defect mode goes to the high-frequency side.These results will contribute a lot to the development of the acoustical instruments.