The investigations about the steady shear viscosity of non-Newtonian flow in concentrated polymer solutions have been reported by Porter et al. and Ozaki et al. Log viscosity versus log molecular weight relations obtained by Porter et al. and by Ozaki et al, are those at constant shear stresses and at constant rates of shear, respectively.In the results obtained by Porter et al., the slope of log η"log M relation becomes smaller as the shear stress increases in the region of molecular weight higher than a critical value Mc as is shown in Fig. 1.On the other hand, the slopes of log η"log M relation obtained by Ozaki et al. are 3.4 in the region of molecular weight lower than a second critical value M'c (>Mc) which depends on shear rate γ0 and <3.4 (nearly 2) in the region of molecular weight higher than M'c as is shown in Fig. 2.Since the concentrated polymer solution spreads a network structure crosslinked temporarily by the entanglement of polymer molecules, it is desirable to make clear the viscosity versus molecular weight relations by making use of the theory of network structure.In § 2 the linear theory of viscoelasticity of network structure is reported in a reformed formalism. When we consider a polymer molecule in the network structure, the aggregation of the remaining molecules could be considered to be a sort of viscoelastic medium. When a part of polymer molecule between the adjacent crosslinkages termed chain, a chain in a molecule has the viscoelastic effects on other chains in the same molecule through the viscoelastic medium, so that the system corresponds to a model composed of interacting Rouse model. The viscoelastic interactions between the chains in a, molecule. though they seems intra-molecular interactions, are due to the average inter-molecular interactions induced by the motion of the viscoelastic medium. By using the above model we obtain the slip equation (2.17) and the stress (2.2'), where <γi> and <Di> contained in τi are viscous and elastic effects in the i-th normal coordinate and are given by (2.19). For continuous distribution of relaxation times, the slip equation and the stress are written as (2.21), which are the expressions in the linear theory.In order to investigate the non-Newtonian effect on viscosity, the linear theory is extended by introducing the parameters depending on the shear stress or rate, and we assume the phenomenological relations (3.1), where α and β are parameters characterizing the elastic and the viscous effects and functions depending only on the shear stress. In non-Newtonian flow, the stress and the slip equation are given by (3.2) and (3.3), respectively. τα is the critical relaxation time corresponding to the movement of molecule having molecular weight Mc, τβ being the maximum relaxation time.For steady flow the stress is given by (4, 2), where γo is the shear rate and ν is the number of chains in the unit volume. The log η-log M relation at constant shear stress is given by (4.3'), where Ms (=Mc) is the molecular weight of chain. From (4, 3'), β is determinable as a parameter depending on shear stress from the experimental results obtained by Porter et al. The experimental data show that as the shear stress increases β decreases from 2.5 to 0.On the other hand β is a function of shear rate and molecular weight, since the shear stress is a function of molecular weight M and shear rate γo.