We have extended the slip-link model originally developed by Doi and Takimoto [Philos. Trans. R. Soc. London, A 2003, 361, 641] to calculate fast shear and uniaxial elongational flows. The original Doi-Takimoto (DT) model shows that steady elongational viscosity increases when the elongational strain rate is larger than Wi(R)((e)) > 1, which is not observed in experiments for entangled polymer melts. To improve the predictions of the DT model, we have extended the DT model by incorporating the stretch/orientation-induced reduction of friction (SORF) developed by Yaoita et al. [Macromolecules 2012, 45, 2773]. Consequently, we can successfully reproduce thinning behavior in steady uniaxial elongational viscosities for fast flows Wi(R)((e)) > 1. Through use of a decoupling approximation, we have found that the reduction of chain stretch has a major effect on the thinning behavior in the strain rate region Wi(R)((e)) > 1 when employing SORF. Meanwhile, under shear flows, the effect of SORF can be observed in a relatively high strain rate region Wi(R)((s)) greater than or similar to 10, where polymer chains start to stretch. Furthermore, we have investigated the statistical properties of the microscopic structure obtained from the DT model for both linear and nonlinear regions. From comparison with the results obtained by the primitive chain network model [Masubuchi et al.J. Chem. Phys., 2001, 115, 4387], we have concluded that the statistical properties of the microscopic structure obtained from the DT model are plausible in the strain rate region Wi(R)((e/s)) less than or similar to 1, but those obtained by the DT model even with SORF in the strain rate region Wi(R)((e/s)) greater than or similar to 1 are questionable because the dynamics of an entangled polymer chain in a time scale shorter than the Rouse relaxation time is ignored in the DT model.