We present new results for the low strain rate behavior of the steady-state planar shear and elongational viscometric functions of model polymer melts, computed by non-equilibrium molecular dynamics simulations. The chain lengths in our model polymer melts vary from N = 2 up to N = 100 beads, the maximum value corresponding to approximately 57 Kuhn lengths (approximately equivalent to polyethylene of molar mass 8300 g/mol). The new results allow us to more precisely evaluate the constants in the third-order fluid constitutive relation that we fitted to the results of our previous simulations. We find agreement between the values of the retarded motion expansion coefficients of terms up to second-order in the strain rate obtained from the two types of flow. This indicates that the second-order fluid model self-consistently describes the stress tensor in shear and elongational flow with a single set of material constants if the deformation rate is sufficiently small. However, we find a discrepancy between two different estimates of a third-order term when it is evaluated from the first and second planar elongational viscosities. The second-order retarded motion expansion is extended to apply to compressible fluids and the deformation rate dependence of the pressure in shear and elongational flows is obtained. The predictions are confirmed by the simulation results. The chain length dependencies of the computed zero shear rate viscosity and first normal stress coefficient agree with the predictions of the Rouse model. The second normal stress coefficient varies as the cube of the chain length and the coefficient of the quadratic term in the strain rate dependence of the shear viscosity is proportional to the sixth power of the chain length for unentangled chains. (C) 2007 Elsevier B.V. All rights reserved.