AbstractThe purpose of this paper is to employ an analytical approach to a two-dimensional viscous flow with a shrinking sheet. A comparative study of the variational iteration algorithm-II (VIM-II) and the Adomian decomposition method (ADM) are discussed. Both approaches have been applied to obtain the solution of a two-dimensional viscous flow due to a shrinking sheet. This study outlines the significant features of the two methods. Comparison is made with the ADM to highlight the significant features of the VIM-II and its capability of handling completely integrable equations. Through careful investigation of the iteration formulas of the earlier variational iteration algorithm (VIM), we find unnecessary repeated calculations in each iteration. To overcome this shortcoming, we suggest the VIM-II, which has advantages over other iteration formulas, such as the VIM, and the ADM. Further iterations can produce more accurate results and decrease the error.