AbstractAn explicit, four‐constant model for viscosity and normal stresses in simple shear has been developed by simplifying the integral theory of Bernstein, Kearsley, and Zapas. In essence the procedure involves curve‐fitting the linear relaxation spectrum. The four constants appear also in equations for the stress distribution and for pressure drop in accelerative flow between flat plates; flow along rays is assumed. The equations reduce to second‐order theory and to Newtonian theory as a Deborah number becomes small. Comparison of the predicted stress distributions with previously published stress birefringent data shows good agreement; because of the low shear rates, however, the check is not demonstrating very strong departures from the second‐order asymptote. Certain other theoretical results, including pressure drop predictions, are als