In this study we address the problem of finding a quantitative mathematical model for the genetic network regulating the stress response of the yeast Saccharomyces cerevisiae to the agricultural fungicide mancozeb. An S-system formalism was used to model the interactions of a five-gene network encoding four transcription factors (Yap1, Yrr1, Rpn4 and Pdr3) regulating the transcriptional activation of the FLR1 gene. Parameter estimation was accomplished by decoupling the resulting system of nonlinear ordinary differential equations into a larger nonlinear algebraic system, and using the Levenberg-Marquardt algorithm to fit the models predictions to experimental data. The introduction of constraints in the model, related to the putative topology of the network, was explored. The results show that forcing the network connectivity to adhere to this topology did not lead to better results than the ones obtained using an unrestricted network topology. Overall, the modeling approach obtained partial success when trained on the nonmutant datasets, although further work is required if one wishes to obtain more accurate prediction of the time courses.