In this work the finite element method is employed to analyze the stability of soil slopes undermined by voçorocas (gulling). Many of the shear slides occurred in both natural slopes and embankments have been caused by the phenomenon of voçorocas, the outcome of a very complex soil erosion mechanism. A brief review about the formation and growing of voçorocas, as well as an overview of their effects on soil slope stability, are made in this work. In the numerical simulation by the finite element method, the potential slip surface is identified through the progressive formation of a region of yielded soil as the erosion process advances. A simple model, consisting of incremental excavations of soil near the foot of the slope, is used in this work to represent the undermining mechanism. Illustrative examples of this technique are presented for some cases of natural soil slopes eroded by voçorocas in the city of Goiania - GO. Numerical difficulties due to the poor convergence of the solution near the soil collapse are also discussed.