The 'semi-indirect' method of Saint Venant is applied to determine directly (i.e. without explicit reference to strains) distributions of stress in complete solids of revolution (e.g. twisted shafts of non-uniform diameter, axially symmetrical systems such as pressure vessels) and in incomplete tores (e.g. helical springs of small pitch, beams of large curvature, and hooks). The paper is intended as a prelude to approximate but general treatment by relaxation methods; consequently only simple examples are considered, but a comparison is made with earlier solutions less suited to a 'relaxation' approach.