This paper describes an analytical formulation and a numerical solution of the elastic dynamic problems of non-homogeneous poroelastic shells of revolution saturated in viscous fluid. The porosity and porous diameter of the material are assumed to be continuously varied along the shell thickness. The equations of motion and the relations between strains and displacements are derived by extending the Sanders shell theory. As the constitutive relations, the consolidation theory of Biot for models of fluid-solid mixtures is employed. The flow of viscous fluid through a porous elastic solid is governed by Darcy's law. In the numerical analysis of the fundamental equations an usual finite difference form is employed for the spatial derivatives and the inertia terms are treated with the backward difference formula proposed by Houbolt. As a numerical example, the simply supported cylindrical shell under a semi-sinusoidal internal load with respect to time is analyzed. Numerical computations are carried out by changing porosity and mean void radius along the shell thickness, and the variations of pore pressure, displacements and internal forces with time are analyzed.