The principal concern of this paper is to focus once again attention on the inherent difficulties which are associated with attempts to determine shear center locations for beams of given cross section on the basis of the classical St. Venant torsion-flexure analysis. The special case of this problem which is given when the beam may be treated as a thin plate of variable thickness is used to bring out the limited significance of the St. Venant formulas in relation to the higher-dimension mixed boundary value problem which has previously been shown to be at the root of the shear center problem.