It is well established that the constitutive equation for a simple material in motions with constant stretch history (csh) can depend only upon the first three Rivlin-Ericksen tensors. The most general explicit form of this result is obtained in this study. Simplifications of this result for planar as well as for axisymmetric flows are listed, though in the latter case only for incompressible fluids. (C) 2003 Published by Elsevier Science B.V.