The properties of both untangled and entangled linear polymer melts under shear flow are studied by nonequilibrium molecular dynamics simulations. The results reveal that the dependence of shear viscosity η on shear rate \documentclass[12pt]{minimal}\begin{document}$\dot{\gamma }$\end{document}γ̇, expressed by \documentclass[12pt]{minimal}\begin{document}$\eta \sim \dot{\gamma }^{-n}$\end{document}η∼γ̇−n, exhibits three distinct regimes. The first is the well-known Newtonian regime, namely, η independent of shear rate at small shear rates \documentclass[12pt]{minimal}\begin{document}$\dot{\gamma }<\tau _{0}^{-1}$\end{document}γ̇<τ0−1 (where τ0 is the longest polymer relaxation time at equilibrium). In the non-Newtonian regime (\documentclass[12pt]{minimal}\begin{document}$\dot{\gamma }>\tau _{0}^{-1}$\end{document}γ̇>τ0−1), the shear dependence of viscosity exhibits a crossover at a critical shear rate \documentclass[12pt]{minimal}\begin{document}$\dot{\gamma }_{\mathrm{c}}$\end{document}γ̇c dividing this regime into two different regimes, shear thinning regime I (ST-I) and II (ST-II), respectively. In the ST-I regime (\documentclass[12pt]{minimal}\begin{document}$\tau ^{-1}_0<\dot{\gamma }<\dot{\gamma }_{\mathrm{c}}$\end{document}τ0−1<γ̇<γ̇c), the exponent n increases with increasing chain length N, while in the ST-II regime (\documentclass[12pt]{minimal}\begin{document}$\dot{\gamma }>\dot{\gamma }_{\mathrm{c}}$\end{document}γ̇>γ̇c) a universal power law \documentclass[12pt]{minimal}\begin{document}$\eta \sim \dot{\gamma }^{-0.37}$\end{document}η∼γ̇−0.37 is found for considered chain lengths. Furthermore, the longer the polymer chain is, the smaller the shear viscosity for a given shear rate in the ST-II regime. The simulation also shows that a characteristic chain length, below which \documentclass[12pt]{minimal}\begin{document}$\dot{\gamma }_{\mathrm{c}}$\end{document}γ̇c will be equal to \documentclass[12pt]{minimal}\begin{document}$\tau _{0}^{-1}$\end{document}τ0−1, lies in the interval 30 < N < 50. For all considered chain lengths in the ST-II regime, we also find that the first and second normal stress differences N1 and N2 follow power laws of \documentclass[12pt]{minimal}\begin{document}$N_{1} \sim \dot{\gamma }^{2/3}$\end{document}N1∼γ̇2/3 and \documentclass[12pt]{minimal}\begin{document}$N_{2} \sim \dot{\gamma }^{0.82}$\end{document}N2∼γ̇0.82, respectively; the orientation resistance parameter mG follows the relation \documentclass[12pt]{minimal}\begin{document}$m_{\mathrm{G}} \sim \dot{\gamma }^{0.75}$\end{document}mG∼γ̇0.75 and the tumbling frequency ftb follows \documentclass[12pt]{minimal}\begin{document}$f_{\mathrm{tb}} \sim \dot{\gamma }^{0.75}$\end{document}f tb ∼γ̇0.75. These results imply that the effects of entanglement on the shear dependences of these properties may be negligible in the ST-II regime. These findings may shed some light on the nature of shear thinning in flexible linear polymer melts.