Free vibration characteristics of a periodically stiffened panel with unconstrained viscoelastic damping layers applied to the flanges of the stringers are analyzed by using the wave propagation approach. Periodic structure theory in conjunction with the concept of damped forced waves is used in the determination of resonant frequencies and the associated loss factors of the composite structure. The complex nature of the rotational and transverse stiffnesses of the stringers is taken into consideration in the analysis. Numerical results showing the effect of the geometric and material properties of the damping layer treatment on the resonant frequencies and loss factors of the composite panel are presented. © 1984.