This semi-inverse method is similar to that used in the so-called Saint-Venant problem for cylindrical three-dimensional first-gradient linear homogeneous and isotropic materials. This semi-inverse method is similar to that used by Saint-Venant to solve the omonimus problem for cylindrical three-dimensional first-gradient linear homogeneous and isotropic materials. Two examples are also presented. It is found that wedge forces are necessary to maintain the body in equilibrium and that these are not an artefact of the double application of the divergence theorem in the second-gradient material derivations.