The free, undamped vibration analysis of a shell of general shape is formulated with a curved isoparametric trapezoidal finite element, including thickness shear deformations and without neglecting z/R in comparison with unity and rotatory inertia effects with consistent mass matrix. The shell element with eight nodes and 40 d.f. is applicable for both thin and moderately thick shell analysis. The accuracy and efficiency of this proposed finite element are illustrated by examples and the results are compared with those obtained by other analytical and numerical methods. The comparisons show that the method yields very good results with a relatively small number of elements. (C) 1997 Elsevier Science Ltd.