The objective of this research was to develop a mathematical model for batch photoautotrophic cultivation of Arthrospira platensis and to validate it against data obtained in experiments. All trials were carried at 30°C, under a light intensity of 60 or 120 µmol m-2s-1. The purpose of the model was to determine the optimal concentration of carbon dioxide, as well as to investigate the formation of phycocyanin. For the experimental conditions in this study, the optimal concentration carbon dioxide (0.8% CO2, v/v) was predicted using the model according to the initial bicarbonate level, the carbon uptake by the microalga, the pH, and the mass transfer process. The use of this optimal value in the gas inlet seems to be a suitable option for maintaining the optimal pH (9.5), thereby eliminating the need for a pH controller in the bioreactor system. According to the simulations, the mass fraction of the phycocyanin formation rate seems to depend on the internal light level. The percentage of adjustment obtained (R2) was ?75%. The velocity of phycocyanin formation was enhanced at intensities up to 120 µmol m-2s-1. However, the actual internal irradiance values were lower than the light compensation point (4.5 µmol m-2s-1), so phycocyanin formation ceased. The mathematical model may facilitate the examination of optimal carbon delivery, as well as the light input, in several A. platensis culture conditions aimed at phycocyanin production.