Abstract: In this paper, the problem of nonlinear buckling of cylindrically orthootropic spherical shallow shells under transverse load is discussed by use of revision iteration method introduced by references¹, and analytical solution of the problem is obtained. In the course of solving, Kirchhoff's supposition of classical plates and shelles theories is given up and therefor the effect of transverse shear deformation on bending deformation is considered. Calculation results show the theoritical analysis and numerical results are crrect and as far as cylindrically orthotropie composite material plates and shells, the effect of transverse shear deformation is worth notice.