A part of non-Newtonian fluids are yield stress fluids. They require a minimum stress to flow. Below this minimum value, yield stress fluids remain solid. To date, 1D and 2D numerical models have been used predominantly to study free surface flows. However, some phenomena have three-dimensional behaviour such as the appearance of the limit between the liquid regime and the solid regime. Here the aim is to use a Computational Fluid Dynamics (CFD) to reproduce the properties of the free surface flow of yield stress fluids in an open channel. Modelling the behaviour of the yield stress fluid is also expected. The numerical study is driven with the software OpenFOAM. Numerical outcomes are compared with experimental results from model experiment and theorical predictions based on the rheological constitutive law. The 3D model is validated by evaluating its capacity to reproduce reliably flow patterns. The depth, the local velocity and the stress are quantified for different numerical configurations (grid level, rheological parameters). Then numerical results are used to detect the presence of rigid and sheared zones within the flow.