- A model for the dynamic behavior of a laminated composite shallow arch is developed from shallow shell theory. Linear equations of motion are derived for thin, moderately thick and thick arches. Free vibration of the arch is explored and exact natural frequencies of the third-order, second-order, first-order and classical arch theories are determined for various boundary conditions. A generalized modal approach is presented to solve the dynamic response of cross-ply laminated arches with arbitrary boundary conditions and for arbitrary loadings. The Poisson effect and rotary inertia are incorporated in the formulation of the arch constitutive equation, in the analytical approaches and in the numerical results. 1997 Elsevier Science Ltd. All rights reserved.