Abstract Urban areascomprising natural terrainare prepared empirically for the urbanistic developmentof cities, causingalterationsto the natural relief and affecting notablythe physical surroundingsas resultof deficient planning in the preparation of the terrainfor urbanism works. Thisstudyseeks to formulate a rational solutionto earth movementsthroughtwomodels, one having to do with simulation and the other being mathematical in contrast with thecurrent empirical methodappliedin numerous works of engineering, where el budgethas an important specific weight. In response to this, modelingofsurfaces emerges, which describesthe process ofphysical and artificial representationof the skin of the earththroughageometric model. Thistype ofmodel permits designing the modificationof a terrain’s topographyto prepare it optimally for a given purpose, considering twofundamental variables: area and volume. As resultof this research, an optimization model was obtained for the designofartificial earth movementsapplicableto the type oftopography prevalent in the citiesin the Colombian Eje Cafetero (coffee growing region). The studyfound that the variables ofarea, volume and cut and fill heights createa model, which determinesthe optimal point and around such, an uncertainty zonecalled design zone, achieving the greatest useful areain the constructionwith the least volumeof earth to move.