In accordance with the memory function of Gaussian chain constraints In entangled polymer melts a set of material Functions related to a certain ＇＇test flow＇＇ are formulated from the O-W-F type constitutive equation by the appropriate selection of the Cauchy-Green and Finger tensors. The dependences of these material functions on the strain rate and the dependences of the linear viscoelastic functions on the primary molecular weight distribution and the entanglement sites sequence distribution on polymer chain are derived from a multiple-entanglement model and a couple of mechanisms of relaxation for the loop and terminal entanglement sites. When the primary polymer chains are modelled with the Lansing-Kraemer molecular distribution function, a set of new relationships among linear viscoelastic functions (eta(0), psi(10)(o), eta(ext)(o) and tau(l)) and the molecular weights and their distribution are formulated. These functions and relationships are verified with experimental data.