The laminar and turbulent flow over a backward-facing step placed in a square duct was investigated numerically. The aspect ratio of the step(step width/step height) was 3 and area expansion ratio was 2:3. Three-dimensional effects were significant due to the small aspect ratio. To simulate turbulent flows, both a standard k-ε model and a non-linear k-ε model were employed and the results were compared. The non-linear model was found to yield better results. From the numerical results, the existence of the corner vortex and the flow field associated with it were clarified. The reattachment length of the three-dimensional flow was found to be considerably shorter than the corresponding two-dimensional flow. The evolution of longitudinal vortices was visualized. Surface flow patterns which clearly demonstrate three-dimensional aspects of the flow were presented. Based on various data available, topological flow pattern was also sketched. To support the findings explored in the present work, experimental data were compared with the numerical data where applicable.