In this paper, the vibration and stability or orthotropic conical shells with non-homogeneous material properties under a hydrostatic pressure are studied. At first, the basic relations have been obtained for orthotropic truncated conical shells, Young's moduli and density of which vary Continuously in the thickness direction. By applying the Galerkin method to the foregoing equations, the buckling pressure and frequency parameter Of truncated conical shells are obtained from these equations. Finally, carrying out some computations, the effects of the variations of conical shell characteristics, the effects of the non-homogeneity and the orthotropy on the critical dimensionless hydrostatic pressure and lowest dimensionless frequency parameter have been Studied, when Young's moduli and density vary together and separately. The results are presented in tables, figures and compared with other works. (C) 2008 Elsevier Ltd. All rights reserved.