Abstract: An asymptotic distributed transfer function method for linear elastic static and dynamic analysis of conical shells is presented. In this method, three shell displacements are first expanded in Fourier series in the circumferential direction, then an infinite number of decoupled partial differential equations containing a spatial variable and a time variable are obtained. Using Laplace transform with respect to time t, these partial differential equations can be simplified to ordinary differential equations containing a complex parameter s, and these ordinary differential equations' coefficient are the functions of spatial variable x. Takingε = L／r₀sinα as a small parameter, the perturbation method has been used to obtain a series of constant coefficient ordinary differential equations. The distributed transfer function method is employed to solve the equations. Combined shells composed of several conical shell segments are then synthesized using the transfer functions of sub-segments. Numerical mathods are presented and compared with that of finite element method.