Abstract Composite materials reinforced with long fibers can have a unique characteristic: distortion of the reinforcing fibers into wavy patterns which may be beneficial or deleterious, depending on the applications. The effect of the resulting smooth periodic stiffness variation in the material on wave propagation along the fiber direction is the focus of this study. The problem of wave propagation in a material with a smooth periodic stiffness variation is simplified by assuming that the stiffness variation is sinusoidal. The simplified problem is studied by means of an analytic small-perturbation method and a numerical finite-difference scheme. The perturbation analysis reveals that there is a critical excitation frequency for a wavy stiffness material at which resonance occurs in the propagating waves. The finite-difference simulation corroborates the presence of resonance effects at and around the critical frequency. The resonant growth of the propagating waves could result in premature fatigue failure, due to resonance increased loading, or sudden unexpected failure if the resonance induced stresses are large enough.