The analytical models for the design of automatic guided vehicle systems (AGVs) available in the literature are limited to the computations of the fleet size and the design of the guide path layout. Another major design factor which affects the performance of an AGV system is the locations and the dimensions of the control zones. The control zones facilitate congestion free flow of AGVs along the guide path. A proper design of the control zones is extremely important for the functioning of the AGV system. When the effects of the control zones are included in an analytical model, its solution procedure becomes complicated and difficult to be solved. This is due to the various interactions between the work stations and AGVs caused by the control systems. In this thesis, Petri net theory is introduced as an alternative method for the modeling of AGV systems. It is a graph theoretic tool which can easily capture synchronization and resource sharing situations which are common in AGV systems. Further, well developed mathematical procedures are available to analyze them. A systematic Petri net modeling procedure for AGV systems using sub nets is provided in this thesis. The Petri net model is used to compute the fleet size and the control zone dimensions of the AGV system.