In this paper, dynamic analysis of the composite truncated sandwich conical shells (STCS) with various boundary conditions subjected to low velocity impact was studied analytically, based on higher order sandwich panel theory. Impact was assumed to occur normally over to the top face-sheet and the contact force history is predicted using two solution models of the motion are derived based on Hamilton’s principal by considering the displacement continuity conditions between the layers. In order to obtain the contact force and the displacement histories, the differential quadrature method (DQM) is used. In this investigation, the effect of different parameters such as number of layers of the face sheets, boundary conditions, semi vertex angle of the cine, impact velocity of the impactor on the impact response from complete model are studied.