Abstract: To understand better the numerical results of loudspeakers,the uniformly valid general solutions are studied analytically for axisymmetric vibration of loudspeaker conical shells in the whole loudspeaker frequency range,which are presented in the form of special functions.At typical low frequencies the bending solutions appear only as the boundary layer effect;in the typical turning-point range they exist in the outer part of the shell outside the turning point;at typical high frequencies they cover the whole loudspeaker shell.The membrane solutions and the bending solutions are coupled each other in the turning-point range,and this coupling shows that one can not eliminate the partition vibration in loudspeaker shells.