Language extinction as a consequence of language shifts is a widespread social phenomenon that affects several million people all over the world today. An important task for social sciences research should therefore be to gain an understanding of language shifts, especially as a way of forecasting the extinction or survival of threatened languages, i.e., determining whether or not the subordinate language will survive in communities with a dominant and a subordinate language. In general, modeling is usually a very difficult task in the social sciences, particularly when it comes to forecasting the values of variables. However, the cellular automata theory can help us overcome this traditional difficulty. The purpose of this article is to investigate language shifts in the speech behavior of individuals using the methodology of the cellular automata theory. The findings on the dynamics of social impacts in the field of social psychology and the empirical data from language surveys on the use of Catalan in Valencia allowed us to define a cellular automaton and carry out a set of simulations using that automaton. The simulation results highlighted the key factors in the progression or reversal of a language shift and the use of these factors allowed us to forecast the future of a threatened language in a bilingual community.