This project report is an attempt to find better conditions and reaction parameters for the potential commercialization of the enzymatic production of amoxicillin. A kinetic model from the literature was used to describe a reaction between p-hydroxyphenylglycine methyl ester (PHPGME) and 6-aminopenicillanic acid (6-APA) that is catalyzed by penicillin G acylase immobilized onto glyoxyl-agarose gel beads. A C++ computer program was developed using the Fourth Order Runge-Kutta method to simulate higher substrate and enzyme concentration during the reaction. For model validation, simulation results were compared with experimental data from the literature and fractional errors. This simulation model predicted 24% yield of amoxicillin at high substrate concentration (50mM of 6-APA; 300mM of PHPGME). It also predicted that increasing the enzyme concentration by four fold could produce a similar amoxicillin yield four times faster. The simulation results obtained in this work could be used in the future to aid in optimization and in further modifications of the kinetic model to predict even better yields. This enzymatic process could therefore become an industrial process to substitute the existing chemical route, which contains toxic organic solvents.