Abstract: The axisyjnmetric buckling behaviour of orthotropic shallow thin conical shells under uniformly distributed loading is investigated. The edges of the shell are assumed to be clamped and movable. The approximate formulas for critical load are obtained by perturbation technique. The perturbation parameters relating to the deflection of cone apex and the angle included between the generator of the shell and the base circle are selected. Numerical results are obtained for three types of fiber-reinforced composite shallow thin conical shells. The effect of material properties on the buckling behaviour is illustrated graphically and discussed. Results obtained in this paper can be used in engineering design.