Bioprosthetic materials, either natural or synthetic, are treated with trivalent aluminum or iron cations, or salts, to prevent in vivo calcification. Such bioprosthetic materials include porcine aortic valve leaflets, bovine pericardium, aortic homografts, biocompatible elastomers, and the like which are intended for invasive, or in-dwelling use in a human or animal body. Simple incubation of the natural bioprosthetic materials in an ion-containing solution, such as aqueous AlCl.sub.3 or FeCl.sub.3, prior to implantation has been found to inhibit calcification of the biomaterial over a prolonged period, and to do so without adverse side effects. Incorporation of an aluminum-containing compound into the formulation for polymers, such as polyurethane, has also been found to inhibit calcification with no adverse side effects.