We deal with the flexure (flexion inegale) of a Saint Venant cylinder whose sections we call Bredtlike with variable thickness. We consider a family of sections Dc whose thickness is scaled by a parameter c. This scaling allows for the construction of an soneparameter family of coordinate mappings from a fixedplane domain D onto ZDe. We represent the Helmholtz operator in D) in terms of a fixed system of coordinates in D and represent the shear stress field in what we call the Bredt basis field, which is not the natural basis associated with any coordinate system. Assuming that the shear stress admits a formal C power series expansion, we obtain a hierarchy of perturbation problems for its coefficients, finding the wellknown Jouravski formula at the lowest iterative step and obtaining its generalization at higher stepsthat is, when the section becomes thick. Similar results are obtained for the warping, the resultant shear stress, and the shear shape factors.