Abstract: This paper deals with the problem of nonlinear axisymmetric buckling for a conical sandwich shell which is composed of orthotropic composite skins and a soft core under the action of uniform pressure. The fundamental equations of the nonlinear stability for conical sandwich shells are derived by means of calculus of variations. An analytic solution for the critical buckling pressure is obtained by use of modified iteration method . Numerical results are obtained for conical sandwich shells with three types of fiber-reinforced composite skins. The effects of geometric and physical parameters on buckling behavior are illustrated and discussed.