Combined shells, cylinder-cone cylinder-plate and stiffened shells are analysed for their free vibration characteristics using a higher-order semi-analytical finite element. A shell theory with thickness normal strain and thickness shears is used for the solution. Natural frequencies of stiffened shells are compared using two approaches: (i) with a discontinuous radius of curvature, i.e. the radius of curvature varies in steps and (ii) continuous radius of curvature, but eccentric thickness. In this the shell element is assumed to be made up of two layers. It is found that the latter approach is more accurate than the first. The effect of various geometric and material properties on natural frequencies are investigated in this study. © 1993.