An alternate form of the Chernin type equations for laterally loaded shells of revolution is obtained. Except for terms of order of the inherent error in shell theory, the final two coupled second order ordinary differential equations are remarkably similar to the Reissner-Meissner type equations for problems involving axi-symmetric stress distributions. Unlike all previous versions, our two equations can be further reduced (just as in the case of axi-symmetric stress distributions) to a single second order equation for a complex stress function without any additional approximation for uniform cylindrical, spherical, conical and toroidal shells. The side force and tilting moment problem for a shell frustum is shown to be the static geometric analogue of the problem of asymmetric bending and twisting of a ring shell sector. An efficient method for the evaluation of the overall influence coefficients is discussed. The stress state of a complete uniform spherical shell subject to concentrated side force and tilting moment at the two poles is analyzed.