Although heart valve replacement is among the commonest cardiovascular surgical procedures, their outcome is often difficult to predict. One of the reasons is the design and choice of material of construction of the prostheses. This thesis describes the use of a mathematical modeling approach in prosthetic heart valve (HV) design. We examined the closing phase behavior of the bileaflet mechanical heart valve (MHV) and demonstrated that it possessed high regurgitation flow and high impact force between the pyrolytic carbon valve leaflet and the housing. The potential problem of valve failure due to crack propagation in the brittle pyrolytic carbon leaflet was also studied. We determined that the initial flaw size was the most important factor determining failure. These studies suggest that although bileaflet MHV performs satisfactorily, there are justifications for improvement. Since the native aortic HV is trileaflet and made of anisotropic and hyperelastic tissue, our approach to a better MHV design is based on our ability to closely mimic the natural geometry and biomaterial properties. A new formulation of the anisotropic poly (vinyl alcohol) - bacterial cellulose (PVA-BC) nanocomposite was developed that possessed mechanical properties similar to that of the porcine aortic leaflet tissue. In the new MHV design, a constitutive model for the leaflet structure based on the anisotropic PVA-BC nanocomposite was developed. Leaflet geometry was designed using an advanced surfacing technique based on the Bezier surface approach. A hybrid element, combining the isotropic hyperelastic element and spar element was created to model the anisotropic PVA-BC nanocomposite in a finite element approach. The final model was examined in terms of mechanical stresses, bending moment distribution and valve dynamics. Principal stress and bending moment distribution are consistent with the collagen fiber distribution in the porcine valve leaflet which provides confidence in the model developed. The simulated valve dynamics patterns formed at various stages of a cardiac cycle are in good concordance with images isolated from a cardiac ultrasound video sequence. These results lend further confidence to the model developed. This model would be suitable for the design of a mold for prototype construction for further evaluation.