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Quantitative analysis on the impacts of human activities on environment is one of the highlights in the research field of sustainable development. In this paper, the IPAT equation were introduced as well as its expanded models including ImPACT model, STIRPAT model, IPBAT model, ImPACTS model and IES model. A model about the relationship between utilization efficiency of grassland resources and economic growth was analyzed based on three different schemes in the Gannan pastoral areas in Gansu Province. The data reflected that the conditions of economic growth was the drop rate of grassland resources consumption per unit GDP satisfied to the equation ttk (critical value). As t is closed to tk during 1985-2004 in the area (t=2.559%, tk=2.693%), the utilization ways of grassland resources are considered to be sustainable.