We show how to transform a large class of differential constitutive models into an equation for the (matrix) logarithm of the conformation tensor. Under this transformation, the extensional components of the deformation field act additively, rather than multiplicatively. This transformation is motivated by numerical evidence that the high Weissenberg number problem may be caused by the failure of polynomial-based approximations to properly represent exponential profiles developed by the conformation tensor. The potential merits of the new formulation are demonstrated for a finitely-extensible fluid in a two-dimensional lid-driven cavity at Weissenberg number Wi = 5. (C) 2004 Elsevier B.V. All rights reserved.