A numerical experiment has been carried out on a fully developed turbulent flow in a square duct. Special attention is given to clarify the effectiveness of the algebraic stress models treated by Launder-Reece-Rodi (LRR) and Gibson-Launder (GL) in explaining the secondary flow of the second kind. The results favor the LRR model over the GL model in comparison with the experiment. The computational time for an algebraic stress model is not much greater than that of the k-ε model.