An analytical technique is developed for the determination of the frequency response matrix of a one-dimensional periodic structure. The detailed analysis is carried out for a periodic Bernoulli-Euler beam on many elastic supports, a simplified version for a skin-stringer panel system commonly used in flight vehicle designs. It is shown that considerable simplification can be achieved by introducing one of several possible interior singular conditions. Finally, numerical examples are given for an undamped system and for the same system with damper units attached at periodic locations.