Armington elasticities are a key parameter in applied general equilibrium models, more so in those models used to analyze free trade agreements and other trade related issues. However, frequently only educated guesses, or extrapolated figures, are used to run the models, and Mexico has not been an exception. In this paper, given the quantity and quality of available data from the Mexican Statistics Institute, we consider the Maximum Entropy approach to be a suitable tool to estimate such elasticities for Mexico. Using annual time series from 1988 to 2004, we estimate the Armington elasticities using the 72 Activities disaggregation level of the System of National Accounts of Mexico (SNAM). Specifically, we use three main model specifications to estimate short run and long run elasticities. The first model is just the simplest regression in levels, while the second one is a partial adjustment model, and the third one an error correction mechanism model.