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In this research, the dynamic stability of an orthotropic elastic conical shell, with elasticity moduliand density varying in the thickness direction, subject to a uniform external pressure which is a power functionof time, has been studied. After giving the fundamental relations, the dynamic stability and compatibilityequations of a nonhomogeneous elastic orthotropic conical shell, subject to a uniform external presure, havebeen derived. Applying Galerkins method, these equations have been transformed to a pair of timedependent differential equations with variable coefficients. These diferential equations are solved usingthe method given by Sachenkov and Baktieva (1978). Thus, general formulas have been obtained for thedynamic and static critical external pressures and the pertinent wave numbers, critical time, critical pressureimpulse and dynamic factor. Finally, carrying out some computations, the effects of the nonhomogeneity, theloading speed, the variation of the semi-vertex angle and the power of time in the external pressureexpression on the critical parameters have been studied.