The elastic nonlinear behavior of imperfect circular cylindrical shells under axially compression has been investigated using nonlineair Ritz analysis. It is shown that the lowerbound of elastic buckling loads for increasing the amplitude of initial geometric imperfections exists. The present lowerbound from nonlinear buckling analysis is in good agreement with the estimation of the reduced stiffness method which provides a simple but safe extension to classical bifurcation analysis for the design of even axially compressed orthotropic cylinders.