||The aim of this work is to predict numerically the turbulent flow through a straight square duct using a nonlinear stress-strain model. The paper considers the application of the Craft et al.’s model [Craft, Launder, and Suga (1996)] to the case of turbulent incompressible flow in a straight square duct. In order to handle wall proximity effects, damping functions are introduced. Using a priori and a posteriori investigations, we show the performance of this model to predict such flows. The analysis of the flow anisotropy is made using the anisotropy-invariant map proposed by Lumley and Newman [Lumley and Newman (1977)]. This map shows the various possible states of the turbulence. The mean flow field and the turbulent statistics are compared with existing numerical and experimental data for square and rectangular duct flows. Overall, the model performance is shown to be satisfactory. In particular, the mean secondary velocity field and the streamwise vorticity are well predicted.