A tissue prosthesis 100 comprises an envelope 38 of a biologically inert, elastically deformable material capable of being expanded to conform to an interior surface of a cavity 36 formed at a site 10 in a patient's body. A filler material 60 is received in a fluent state in the envelope 38. The filler material 60 is of the same class of material as the envelope 38 to form, when cured, together with the envelope 38, a unified structure.