Recent studies suggest that flexural stresses induced during the opening phase may be responsible for much of the mechanical failures of bioprosthetic heart valves. Sharp leaflet bending is promoted by the mounting of valves on rigid stents that do not mimic the systolic expansion of the natural aortic root. We, therefore, hypothesized that flexural stresses could be significantly reduced by incorporating a flexible or expansile supporting stent into the valve design. Using our own non-linear finite element code (INDAP) and the pre- and post-processor modules of a commercial finite element package (PATRAN), we simulated the opening and closing behaviour a trileaflet bovine pericardial valve. The leaflets of this valve were assumed to be of uniform thickness, with a non-linear elastic behaviour adapted from experimentally obtained bending stiffness data. Our simulations have shown that during maximal systolic valve opening, sharp curvatures are induced in the leaflets near their commissural attachment to the supporting stent. These areas of sharp flexure experience compressive stresses of similar magnitude to the tensile stresses induced in the leaflets during valve closure. By incorporating a stent with posts that pivot about their base, such that a 10% expansion at the commissures is realized, we were able to reduce the compressive commissural stressing from 250 to 150 kPa. This was a reduction of 40%. Conversely, a simple pliable stent with stent posts that deflect inward and outward under load did not achieve a significant reduction of compressive stresses. This numerical analysis, therefore, supports the theory that (i) high flexural and compressive stresses exist at sites of sharp leaflet bending and may promote bioprosthetic valve failure, and (ii) that proper design of the supporting stent can significantly reduce such flexural stresses.