A new refined but simple shear deformation theory of elastic shells is developed for shells laminated of orthotropic layers. To evaluate the new displacement field assumed which is justified in plates from the three- dimensional elasticity theory, classic types of shallow shells are considered. The boundary value problem is formulated by making use of the principle of virtual power in conjunction with the assumed consistent displacement field. The Navier type exact solutions are presented in statics and in vibrations for cylindrical and spherical shells under simply supported edge boundary conditions.