The batch production of antibiotic by Penicillium chrysogenum is modeled using phenomenological and empirical approaches. In the phenomenological approach, the fungal growth is described by the logistic law, a substrateindependent model for microorganism population dynamics. In addition, the production of penicillin is also modeled considering that the formation of antibiotic is not associated with cell growth and that the product is degraded by hydrolysis according to first-order kinetics. From two sets of experimental data extracted from the literature regarding the batch cultivation of the fungus under different initial cell concentrations (0.18 and 0.40%-DW), it was possible to estimate the model parameters using one of the sets, while the model validation test was performed using the other set. The phenomenological model satisfactorily described the behavior trend of the modeled state variables; however, there is need to obtain a larger amount of experimental data in more diverse initial conditions to achieve a better estimation of parameters and a better description of the bioprocess phases. In the empirical approach, sigmoidal models were adjusted to describe the temporal profiles of cell and product concentrations. The empirical models were successful in describing the bioprocess behavior and appeared quite viable for the modeling of complex bio-systems, such as those comprising the production of antibiotics by filamentous fungi. The parameters of the mathematical models generated by each approach were statistically significant at a confidence level of 95%. Relationships between the growth kinetic parameters of the phenomenological model and those of the empirical model were established.