The invention concerns an assembly comprising a valve prosthesis to be implanted and a support receiving said valve. The support comprises: at least a tubular portion made of a pliable material slightly stretchable in the circumferential direction; means for fixing said tubular portion to the wall of the corporeal duct; and a plurality of elongated reinforcing elements, arranged on the circumference of said tubular portion and linked to said tubular portion independently of one another; the valve is linked at least partly to said elongated reinforcing elements, in particular at the commissures of its leaflets, and said elongated reinforcing elements jointly form, in extended position, a structure having a predetermined diameter that ensures sufficient extension of said valve.