This paper presents a study of a novel vane pump power split transmission (VPPST). The transmission incorporates a new component, the Vane Power Split Unit (VPSU). The VPSU is a double-acting vane pump with a floating ring where the input shaft is connected to the engine and the floating ring is connected to the output shaft. The VPSU generates hydraulic oil flow at a rate proportional to the difference in angular velocities between the input and output shafts. This flow enters a hydraulic motor mounted to the output shaft. The vane pump power split transmission (VPPST) is a combination of the double-acting vane pump (VPSU) and the hydraulic motor directly connected to the pump. A CFD model of the VPSU has been created to better understand its performance. The model uses the three-dimensional CFD commercial code PumpLinx®, developed by Simerics® Inc. Thanks to collaboration with the code developers, the model is able to predict the complex fluid dynamics in the pockets in the rotor into which the vanes retract. These pockets are referred to as under-vane volumes. The rotor of the vane pump, in fact, has several internal channels that connect the pumping chambers between the vanes to the under-vane volumes. The combination of the vanes and the internal ducts and volumes of the under-vanes have been modelled as dynamic "valves" that rotate with the rotor. In this way the radial movements of the vanes are computed as a part of the simulation, based on the pressures due to the compression of the volumes on the inner diameter side of the vanes. The study is a result of collaboration between the University of Minnesota and the University of Naples "Federico II" research groups and the code developers of Simerics® Inc. The universities and Simerics® Inc. have all been involved in this project, working in close cooperation for the model building and simulations.