The unsteady unidirectional flow problem of a non-Newtonian fluid is investigated by the Network Simulation Method (NSM). The analytical solution introduced by Hayat et al. (2000) [23] has been presented graphically. On the other hand, the provided solution by the network method has also been explained and analyzed. Our aim is to compare both solutions to demonstrate the excellent degree of agreement between the numerical results of Hayat et al. (2000) [23] and the results provided by the NSM. The effect of the parameters such as dynamic viscosity, diffusion coefficient and density involved are reflected in the graphs. Velocity graphs are presented for various values of dimensionless time and spatial coordinates.