This work concerns numerical simulations of Power-law fluids. This non-linear problem is solved by using the Asymptotic-Numerical Method (ANM). As this problem is strongly non-linear, we show how the ANM can be used (introduction of new variables, regularization parameter). A numerical method to compute critical Reynolds numbers, bifurcation points, is also proposed. This method makes it possible to determine accurate critical Reynolds without increasing the computational times. Several numerical examples help to demonstrate the efficiency and the reliability of the proposed methods. (C) 2013 Elsevier B.V. All rights reserved.