If algae are to be considered as an economical alternative feedstock for biodiesel and other renewable fuels, an efficient cultivation method needs to be designed. In theory, all algae needs to grow are sunlight, carbon dioxide and some trace elements. One method of cultivation currently being considered is the photobioreactor. A complete mathematical model of the system would be useful to analyze and improve the productivity, efficiency and economics of the reactor. To date there is no such model of the growth kinetics as a function of light intensity which varies in the reactor both as a function of distance from the source and cell concentration. The objective of the current work is to model the algal growth in a novel external loop airlift reactor as a function of light intensity and shear stress to aide in the improvement of the design of the photobioreactor. The photosynthetic factory model proposed by Eilers and Peeters (1988) is used to determine which cells are photosynthetically active. The variation in the light intensity is modeled initially using the Beer-Lambert equation, and then modified using experimental data. The geometry of the system is also considered in the modeling of the growth kinetics. All the equations were solved using Matlab.