A mathematical model was developed to analyze beef production systems in Southern Chile. The study considered the identification of the main components of systems under different beef steer management strategies, using pasture with or without supplementation and back grounding cattle on pasture followed by a winter period of confined feeding with pasture silage and concentrates. Validation of model outputs using 200 kg LW Hereford steers against real experimental data showed no significant differences (P ≥ 0.01) between simulated and observed final weights. In order to analyze the interaction between the stocking rate (SR) and supplementation, three SR of 2, 2.5 and 3 steers ha-1 with and without pasture silage supplementation at the rate of 5 kg DMd-1 steer-1 for the length of the entire period were simulated. Means were compared by the least significant difference (LSD, P ≤ 0.05). Significant differences were found in terms of final weights, which decreased with increasing SR regardless of the supplementation level, although silage supplementation tended to reduce differences between SR. A second set of simulation runs was carried out to simulate on-farm finishing of the steers through a final phase of confined feeding based on a ration of silage and concentrates. Final weights differed between SR and systems and results showed that the optimum corresponded to 2.5 steers ha-1, since at this SR the largest income corresponded to the smallest mean cost. It is concluded that a stocking rate of 2.5 steers ha-1 is feasible if winter supplementation is available, independently of a finishing period in feedlot.