The vibrations of shells of general shape are analysed using finite element method. A curved isoparametric trapezoidal finite element, which includes thickness shear deformations and without neglecting z/R in comparison with unity and rotatory inertia effects with consistent mass matrix, is presented. An eight-noded element with five degrees of freedom per node is used. Hamilton's principle and Wilson-theta integration method are applied for deriving the equations of motion and the solution of these equations, respectively. Several examples are presented and the results are compared with those obtained using other solution techniques. (C) 2004 Elsevier Ltd. All rights reserved.