The ethanol production process by Saccharomyces cerevisiae in a batch reactor was studied aiming to propose mathematical models able to predict the behavior of yeast, substrate and product concentrations throughout the fermentation time and to estimate the parameters of the proposed models. Two kinetic models were tested and solved in DASSL subroutine implemented in FORTRAN. The kinetic parameters of each of the proposed models were estimated using the ESTIMA, which is based on heuristic algorithm of particle swarm and Gauss-Newton method. The objective function adopted was the least squares. The model purpose, with a cell death term presented the best fit among the proposed models and the objective function value was equal to 0.2221. The estimated parameters values were statistically significant and their values were μmax = 0.2124 h-1; k1 = 3.7444 h-1; k = 2.2839 h-1; YX/S = 0.0369; YX/P = 0.0624, KS = 93.4361 g∙L-1 and K0 = 2.5028‧10-3 h-2. This model was able to predict cell death behavior satisfactorily.