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This is a numerical investigation of a yield-stress fluid flowing down an inclined plane. A three-dimensional, free-surface, two-phase incompressible Navier-Stokes solver is extended to handle generalized Newtonian fluids. Special attention is spent on the treatment of the non-Newtonian fluid close to the free-surface and on the boundaries, to get consistent values for the viscosity in those domains. The core of the solver is a projection method that is extended by an implicit solver for the stress terms in order to cope with high viscosities. This numerical tool is tested against experimental data of dam break experiments on an inclined plane, which were conducted in the Laboratoire d'hdraulique environnementale (LHE) at the École polytechnique fédérale de Lausanne (EPFL). After the numerical tool is validated by these experimental data, I investigate the flow structure of a yield-stress fluid inside unsteady flows on the inclined plane and inside the inclined channels. Some typical phenomena like the formation of levees and plug domains are reproduced. As in the numerical simulation all physical variables are accessible, the mechanisms inside these flows is analyzed. Looking at the energy dissipation process shows that for the Herschel-Bulkley fluids most of the energy is dissipated where the local Bingham number is close to one.