The high dependence of rangeland-based livestock farming systems to environmental uncertainty makes the resilience of these systems as important as production. Quantification of resilience is however difficult to conduct in real systems due to their low reproducibility. In this study, we develop a modeling approach to quantify both engineering resilience (return time after a perturbation) and ecological resilience (magnitude of a perturbation that a system can bear) of a mixed herd livestock farming system in Mongolian steppes. The model, build within the framework of the viability theory, captures the dynamics of the herd and its management. The system has the particularity to be impacted by agro-climatic events called thuds that induce massive mortalities when harsh climatic condition and high stocking densities are met. Results show that (i) resilience non-linearly depends on herd composition and the level of underground biomass of the system, (ii) contrasted management strategies may be followed to cope with the risk of dzud and (iii) according to their herd composition most herders of the area can absorb climate shocks unless they compete for forage with other herders. Results are discussed regarding the impact of forage resource sharing on the resilience of these grazing systems.