Molecular theory based scaling arguments relating the extent of entanglement depletion to the prevailing flow intensity are utilized for the quantitative description of the shear thinning rheology of entangled linear polymer solutions and melts. A power law decay with respect to shear rate (gamma (over dot)) is assumed for the viscosity, eta similar to K gamma over dot(n-1), and the first normal stress coefficient, Psi (1) similar to L gamma over dot(m-2). Following experience and the Doi-Edwards molecular theory, the lower rate limit of the non-Newtonian regime is taken equal to the inverse of the relaxation time of the whole chain. By analogy, and consistent with Menezes and Graessley's model for polymer relaxation under fast flow, it is assumed that shear thinning ceases at a characteristic higher rate equal to the frequency of the swiftest entanglement renewal process. Within these two gamma (over dot) limits which define the non-Newtonian regime, estimates for the n and nz exponents are made connecting them to molecular relaxation characteristics. Expressions for the K and L coefficients are also derived, relating them to the molecular weight, chain rigidity, polymer concentration, and temperature.