Most of the turbulence models in the literature contain simplified assumptions which make them computationally inexpensive but of limited accuracy for the solution of separated turbulent flows. Dramatic improvements in computer processing speed and parallel processing make it possible to use more complete models, such as Reynolds Stress Models, for separated turbulent flow simulations, which is the focus of this work. The Reynolds Stress Model consists of coupling the Reynolds transport equations with the Favre-Reynolds averaged Navier-Stokes equations, which results in a system of 12 coupled non-linear partial differential equations. The solutions are obtained by running the PUMA_RSM computational fluid dynamics code on unstructured meshes. The equations are solved all the way to the wall without using any wall functions. Results for high Reynolds number flow around a 6:1 prolate spheroid and a Bell 214ST fuselage are presented. For the prolate spheroid basic flow features such as cross-flow separation are simulated. Predictions of circumferential locations of cross flow separation points are in good agreement with the experiment. A grid refinement study is performed to improve the computations. The fine mesh solution predicted locations of primary and secondary separation points with errors of roughly 2 and 0, respectively. Flow simulations around an isolated Bell 214ST helicopter fuselage were also performed. Predicted pressure and drag force correlate well with the wind tunnel data, with a less than 10% deviation from the experiment. Drag predictions also show relative speed of Reynolds Stress Model compared to Large Eddy Simulation to compute time averaged quantities. For numerical solutions parallel processing is applied with the MPI communication standard. The code used in this study is run on Beowulf clusters. The parallel performance of the code PUMA_RSM is analysed and presented.