Asymmetric vibration behaviour of cantilever conical shells with variable thickness is presented. Love's first approximation thin shell theory is used to analyse isotropic conical shells. Semianalytical finite element method is used to solve the problem. The results illustrate the effect of various parameters on the natural frequencies, especially the lowest natural frequency, of the shells. During the computation, the mass of the shell is retained as a constant for a particular slant length to small end radius ratio. © 1990.