This paper describes efficient C-0-compatible finite elements for modelling structurally damped laminated composite plates and shells under harmonic vibrations. Based upon a shear deformation theory of any order p (PSDT), the elements are well adapted for evaluating, from given elastic and damping properties of the material, the global modal response (mode shapes, natural frequencies and modal loss factors) of multilayered structures. Numerical test cases are presented in order to validate the proposed formulation. Results show that this shell model is accurate and more efficient than the 3D solid formulation for analyzing thin to moderately thick structurally damped plates or shells. (C) 2010 Elsevier Ltd. All rights reserved.