This paper describes an analytical formulation and a numerical analysis of the elasto/visco-plastic problems of orthotropic moderately thick shells of revolution under axisymmetrical loads with application to a cylindrical shell, and with comparison to experimental results. The analytical formulation is developed by extending the Reissner-Naghdi theory in elastic shells with a given consideration to the effect of shear deformation. As the constitutive relation, Hooke's law for orthotropic materials is used in the elastic range, and equations based on the orthotropic visco-plastic theory derived from the orthotropic plastic theory by Hill are employed in the plastic range. The visco-plastic strain rates are related to the stresses by Perzyna's equation. In order to check the adequacy of the numerical analysis, experiments are performed on elasto/visco-plastic deformation of a titanium cylindrical shell subjected to internal axisymmetrical loads. Good agreement is obtained between the experimental results and analytical solutions.