New rheogoniometer data for stress development after initiation of a steady shear are presented for three polymer melts: a low‐density polyethylene, a high‐density polyethylene, and a polystyrene. Three temperatures (160°C, 180°C, 200°C) were studied. Both the shear and normal stresses were found to “over‐shoot” at the higher shear rates. These data are compared in detail with three viscoelastic (constitutive) models: (1) the Bernstein, Kearsley, and Zapas model, using a particular functional form for the memory function; (2) the Bird‐Carreau model; and (3) the Bogue model, as modified by Bogue and White. The general features of these and certain other constitutive models are discussed. The general conclusion is that nonlinearities must be introduced wherever a time constant appears, which can be interpreted graphically as a shift of the relaxation times to lower values. Some comments about the “analogy” between shear rate and molecular weight are also made.