In order to find the sustainable development model and reveal the environmental effects of different development models, this paper provides a theoretical basis for the sustainable development and environment-friendly society construction. This paper establishes a “resourceenvironmenteconomy”(REE) three-dimensional Dynamic system model, and the nonlinear stability of the system is analyzed by nonlinear dynamic theory and numerical simulation. The dynamic behavior of the system is simulated numerically, and the two important factors of pollution emission and resource extraction are studied emphatically to discuss their impact on the system. The results show that the pollution rate and resource extraction rate have a great influence on the system. When the pollution emission rate is in a certain range, the system appears limiting ring and forms the periodic phenomena. When the resource extraction rate is controlled to a certain extent, the economy can achieve a stable level, environmental pollution is also reduced and resource reserves are ensured. This paper has important practical significance to realize the coordinated and sustainable development of “resource-environment-economy”.