A support for a natural human heart valve is disclosed, said support consisting of an annular or part annular semi-rigid frame having the shape of at least a substantial portion of the periphery of said natural heart valve at the base of its cusps, the frame being completely or partly enclosed in a textile sheath, the frame and the sheath being formed of a bio-compatible material and being deformable after implantation. The frame and sheath may be flexurally deformable, and are extensible by 0.001 times to 0.3 times their length. Preferably, the frame has the same flexural elasticity as an annular bundle or 2 to 8 turns of a cylindrical bristle or poly(ethylene terephthalate) and having a circumference equal to 0.025 times the length of one turn. The frame may be formed of at least one strand of bristle. The frame and the sheath may be in the form of a portion of a convex curve.