In this peper, non-symmetrical large deformation problem of a shallow conical shell is studied by two-parameter perturbation method. The third-order approximate analytical solution of the deformation of a shallow conical shell subjected to linear loads is abtained and the characteristic curves of load-deflection on a perturbin point are portrayed. The similar questions of other kind of shell and-plate can be disscussed by using this paper’s method. As the examples, the large deflection of plate and shallow conical shells with different initial deflections is discussed. In this peper, non-symmetrical large deformation problem of a shallow conical shell is studied by two-parameter perturbation method. The third-order approximate solution solution of the deformation of a shallow conical shell subjected to linear loads is abtained and the characteristic curves of The same questions of other kind of shells and-plate can be disscussed by using this paper’s method. As the examples, the large deflection of plate and shallow conical shells with different initial deflections is discussed.