Abstract: A discrete-layer shear deformation theory is used to analyse the free vibration of laminated shells.The theory adopts an assumption that the transverse shear strains across any two layers are linearly dependent on each other. The theory contains the same dependent variables as the first-order shear deformation theory, but the set of governing differential equations is of twelfth order. No shear correction factors are required. Free vibrations of a short circular cylindrical shell and two shallow shells are calculated. The numerical results are compared with the classical lamination theory first-order shear deformation theory and other shear deformation theory solutions.free vibration analysis, laminated shells, transverse shear effects, discrete-layer shear deformation theory