Many mines are moving from conventional tailings storage facilities to filtered tailings disposal systems. The benefits of these systems include increased water recovery, reduced size of containment landfills, improved facility safety, and reduced environmental impact. In geotechnical terms, the challenges are to find the correct way of waste disposal: whether in piles of dry sandy tailings or co-disposal waste rock. The long-term evolution of the surface of fine and sandy tailings stockpiles is a matter of concern. The goal of this study was to quantitatively evaluate the temporal evolution of a paste tailings pile, using a computational model of landscape evolution. For this, SIBERIA, a simulator of the evolution of landscapes under the action of runoff and erosion, was used. The effect of erosion on a trunk-pyramidal tailings pile with about 21% of slope after long periods of decommissioning (100 and 250 years) was studied. The SIBERIA modelling data considered the surface roughness and the average diameter of the sediment particles and the typical properties of iron ore tailings. The results indicate that for a lower Manning roughness coefficient and larger average apparent diameter of the sediment particles (or clods), the lower the sediment transport will be and, therefore, in the long term, the greater will be the integrity of the tailings pile.