The numerical results of investigations of stress-strain state of thin and thick orthotropic shells are set out with taking into account the physical nonlinearity and small and not small shear stiffness of composite materials. On the example of analysis of the spherical shell with the circular hole, the influence of indicated factors on the stresses and deformations distribution according to the shell thickness by assumed models of deformations (Kirchhoff-Love and Timoshenko hypotheses) is studied. On the base of obtained numerical results, the integrating reasoning about the priority of taking into account either physical-mechanical properties of composites and practicability of assumed shell models are given.