A capsule consists of an internal medium (pure or complex liquid), enclosed by a deformable membrane. In Biomedical Engineering, bio-artificial capsules are used in drug delivery systems, artificial organs or cell therapy. A liquid filled capsule is also an appropriate model for a simple cell such as a red blood cell. When capsules are suspended in a flowing liquid, they are deformed by viscous fluid stresses and may sometimes burst. Modeling of this process is necessary for bio-artificial capsule design and control of breakup. A major issue is the determination of the mechanical properties of the membrane, as these control the resistance of the capsule to applied stresses. In many cases the membrane is very thin and treated as a two-dimensional solid with hyperelastic or visco-elastic properties. Popular membrane constitutive laws include the Mooney-Rivlin (MR) law that assumes that the membrane is an infinitely thin sheet of a 3D incompressible material. For membranes with a finite area dilation resistance, a Skalak et al. (Biophys. J., 1973) law (SK) or Evans & Skalak (Mechanics and Thermodynamics of Biomembranes. CRC Press.1980) law (ES) are usually preferred as they account separately for shear deformation and area dilatation of the material. However, MR, SK or ES laws lead to quite different membrane behaviors for large deformations (Barthes-Biesel et al. 2002).