This study is concerned with the interaction of six torsional modes in a composite axisymmetric waveguide whose interfaces are sinusoidally corrugated in the axial direction. The modes are interacting when two resonant conditions on the codirectional modes and a Bragg condition occur simultaneously. In light of the weakness of the interface corrugations, the perturbation method of multiple scales is used to derive the mode coupling equations. A novel numerical scheme for two-point boundary-value problems is used to solve the coupled amplitude equations. The power reflection coefficient of a filter section is then calculated for the cases of uniform, tapered, and chirped corrugations. An optimal filter is realized by combining both taper and chirp thus producing a nearly ideal characteristics.