RELAP5-3D models of the ITER Vacuum Vessel (VV) Primary Heat Transfer System (PHTS) have been developed. The design of the cooling system is described in detail, and RELAP5 results are presented. Two parallel pump/heat exchanger trains comprise the design - one train is for full-power operation and the other is for emergency operation or operation at decay heat levels. All the components are located inside the Tokamak Building (a significant change from the original configurations). The results presented include operation at full power, decay heat operation, and baking operation. The RELAP5-3D results confirm that the design can operate satisfactorily during normal pulsed power operation, decay heat operation and baking operation. All the temperatures in the coolant and in the different system components are maintained within acceptable operating limits.