The Intravenous Membrane Oxygentor (IMO) device is an artificial respirator being developed at the University of Pittsburgh Medical Center (UPMC) with the objective of providing up to 50% of the O2 and CO2 exchange requirements to patients with the Acute Respiratory Distress Syndrome (ARDS) [1-4]. In-vitro and in-vivo experiments and computational simulations at the UPMC and Carnegie Mellon University (CMU), respectively, have been carried out to get a better understanding of the flow and mass transfer characteristics of the IMO [3,4, 7-11]. Numerically obtained pressure drop, for stationary and pulsating balloon conditions, presents a good agreement with the in-vitro experiments [4, 11]. The effect of the balloon pulsation on the flow pattern and mass transfer has also been investigated. Numerical results with a stationary balloon demonstrate a laminar flow regime with no secondary flows [10-11]. These results have indicated that the pulsating balloon generates a 3D oscillatory flow with a strong secondary flow that could increase the flow mixing and the mass transfer rate near the fibers [9-10]. These simulations however, have not considered the curvature of both the fibers and balloon and their effect on the flow mixing and mass transfer characteristics. This article reports numerical investigations of the effect of the curved shape of the balloon on the flow and oxygen transfer pattern of the IMO device shown in Fig. 1(a), for stationary and pulsating balloon regimes.