In this paper we try to build a bridge between the traditional analysis of the evolution of tourism destinations and economic growth theory. With such an aim we develop an environmental growth model for an economy specialized in tourism and we derive the pattern of tourism development with numerical calculations. The results of our simulations do not contradict the general pattern of evolution implied in the Tourism Area Life Cycle Hypothesis, being environmental deterioration and public goods congestion the main reasons for the stagnation of the tourism destination. We also show the importance of the quality of private tourism services in the evolution of the tourism destination.