A methodology is presented for the formulation of an algebraic extra-stress model derivable from the Oldroyd-B constitutive equation for a viscoelastic fluid. An implicit algebraic tensor relation is derived directly from the differential constitutive relation by involving a slow variation condition on the evolution of the deviatoric part of the extra-stress tensor. An explicit solution to this algebraic constitutive equation is then obtained using representation bases developed previously for the turbulent flow of Newtonian fluids. A series of validation flows are then studied to assess the accuracy and range of applicability of the algebraic extra-stress model. (C) 1998 Elsevier Science B.V. All rights reserved.