This book focuses on the use of Large Eddy Simulation (LES) and Reynolds-averaged Navier-Stokes (RANS) to simulate the flow around elliptical bluff body with blunt trailing edge fitted with open base cavity. The main objective of this study is to determine the effects of the cavity on the drag of the body. A secondary but important objective is to demonstrate that LES can provide accurate representation of the flow around this bluff body. Moreover, LES results can complement the available experimental results in order to provide a much better understanding of the flow. The simulations were carried out at a Reynolds number of 2.6×104 based on the height of the body using Spalart- Allmaras RANS model while the LES were performed using Smagorinsky dynamic model.