Abstract <p>This research presents the elastic behavior of rotating, axisymmetric, thick-walled cylindrical pressure vessels made of saturated porous materials. Biot’s law was used to study mechanical behavior instead of Hook’s law. By applying the first-order shear deformation theory (FSDT) and the principle of virtual work, the equations of the problem have been derived. Equations of the problem have been solved by applying the eigenvalue-eigenvector method for clamped-clamped boundary conditions. The effects of the porosity coefficient, Skempton coefficient, and rotational velocity on the mechanical behavior of thick cylindrical pressure vessels have been analyzed. Results demonstrate that by increasing the porosity coefficient and rotational velocity, axial and radial displacements are increased. By increasing the Skempton coefficient, axial displacement remains constant, and radial displacement is decreased. The results indicate that an increase in the porosity coefficient leads to a decrease in the axial, circumferential, and radial stresses. It was observed that with an increase in Skempton coefficient, the axial and radial stresses increase. It was also found that the circumferential stress decreases with an increase in Skempton coefficient. The results showed that with increasing angular velocity, the axial, circumferential, and radial stresses increase in a nonlinear manner. To the best of our knowledge, no author has ever performed such an analysis before.</p>