A mathematical model is presented for the batch production of poly-beta-hydroxy butyrate, a well known biopolymer, from Azotobacter vinelandii utilizing different carbon sources, sucrose and cheese whey. The effect of substrate concentrations and inoculum concentrations on cell mass and P(3HB) production are studied in a batch experiment. Substrate utilization kinetics is also studied. Set of differential equations for cell mass rate, product formation rate, and substrate utilization rate as functions of initial cell concentration, cell concentration at any time and stationary cell concentrations, are used to predict the system behaviour. The kinetic pattern obtained from the batch experiments are used to simulate the models.