A three dimensional CFD analysis of a novel vane pump power split transmission is studied in this paper. The model was built using PumpLinx®, a three-dimensional CFD commercial code developed by Simerics Inc.® The Mathers Hydraulics® vane pump is a double-acting vane pump with a floating ring. By coupling the floating ring to an output shaft, the vane pump becomes a hydrostatic transmission. The focus of this activity is the optimization of the vane pump analyzing the internal fluid dynamics of each part during the pump operation and redesign. The study is a result of collaboration between the University of Minnesota and the University of Naples "Federico II" research groups. The universities involved in this project worked in close cooperation on these simulations. A prototype pump will be tested on a hydraulic test bench at the University of Minnesota, and the experimental data will be used to validate the simulation model.