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 equation, 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 axi-symmetrical loads. Good agreement is obtained between the experimental results and analytical solutions.