The turbulent flow in a straight duct of rectangular cross-section is investigated numerically. The main interest in this thesis is the secondary flow in a developing duct flow. The analysis uses the finite volume method based on the partially parabolized Navier-Stokes equation (PPNS) and the SIMPLE algorithm is adopted for the solution procedure. The algebraric-stress model (ASM) using Rodi's assumption is employed in the present study. Computational results using ASM are compared with experimental data and those obtained using a nonlinear k-ε model. It is found that ASM is superior to the nonlinear k-ε model in predicting the flow near the corner of the duct.