A finite element analysis for the free vibration behaviour of doubly curved shells is presented in which eight-noded curved quadrilateral isoparametric finite elements are used. The first order shear deformation theory for thin and shallow shells is used in the formulation. Results are obtained for comparison with those in the existing literature and to investigate the effects of various composite parameters relevant to doubly curved shells, such as fibre orientations and lamination schemes and several geometrical parameters like aspect ratio, smaller height to greater height ratio (for conoids), thickness to radius ratio (for hyperbolic and elliptic paraboloids), and radii of curvature ratio (for elliptic paraboloids). (C) 1996 Academic Press Limited