A rheological equation for viscoelastic fluids is derived as an expansion of Noll's functional for simple fluids. The present expansion is developed in terms of the deformation rate referred to a co‐rotational material frame. The resulting series of approximations for the stress differs significantly from those proposed previously by Green and Rivlin and by Coleman and Noll. Applications to both simple‐extensional and viscometric flows are considered. For viscometric flows the present model exhibits non‐Newtonian effects similar to those observed in real fluids, with relatively few terms in the functional expansion. The first term in the expansion yields a “first‐order” fluid similar to the model proposed by Pao. Expressions are also given for the viscometric material functions of the present “third‐order” fluid. As with higher‐order fluids, these functions areFourierintegrals of certain hereditary or memory functions for the fluid.