This study considers the dynamic stability of a laminated truncated conical shell with variable elasticity moduli and densities in the thickness direction, subject to a uniform external pressure, which is a power function of time. Initially, the dynamic stability and compatibility equations of a laminated elastic truncated conical shell with variable elasticity moduli and densities, subject to an external pressure, have been obtained. Then, employing Galerkin's method, those equations have been reduced to a system of time-dependent differential equations with variable coefficients. Finally, applying a mixed variational method of Ritz type, the critical dynamic and static loads, the corresponding wave numbers and the dynamic factor have been found analytically. Using those results, the effects of the variations in elasticity moduli and densities, the number and ordering of the layers, the semivertex angle and the power of time in the external pressure expression are studied via pertinent computations. It is observed that these factors have appreciable effects on the critical parameters of the problem in the heading.