Several classes of multiple-mode rheological constitutive equations are tested for fitting and predicting viscoelastic flow properties of a typical low-density polyethylene melt. An optimization procedure is used to fit the phenomenological parameters of each model under consideration to experimental data taken in small-amplitude oscillatory shear flow and steady shear flow. These parameter values are then used to generate predictions for transient shear and uniaxial elongational flow experiments, and the predictions are then compared to experimental data. Model successes and failures are discussed, and the outlook for using rheological equations in real design processes is addressed. (c) 2005 Wiley Periodicals, Inc.