Constitutive relations generally require a large set of fluid relaxation times to provide an accurate fluid description. In situations involving the solution of the dynamic equations of flow simultaneously with the constitutive relation, the use of a single relaxation time model is desirable because of the time consuming nature of the numerical solution schemes. This work presents a single relaxation time fluid model, obtained by empirically modifying the existing form of the Meister model. The empiricisms take the form of two functions of deformation rate, chosen so the model will predict quantitatively the time to maximum overshoot and the magnitude of the maximum overshoot in transient shear stress for a “start‐up” experiment. The modified model compares very well to transient and steady data for five polymer solutions and to the predictions of the Carreau Model B.