AbstractFinite element models provide only approximate results under most loadings. A beam modelled by constant‐strain triangles and loaded by pure moment is a case in point. Yet if the iterative method advanced by Loubignacet al.1is applied to this model, the exact stress field will be generated. The iterative method derives from a parent formulation that can be solved without iteration.2As shown in this paper, the parent formulation contains the sum of two stiffness matrices. One is produced by the customary finite element shape functions. The other is produced by finite difference expressions for strain gradients that are not contained in the shape functions.Loubignac's method produces a stress field that is continous across interelement boundaries. Other methods that seek to impose interelement continuity are noted in the concluding sectio