A multilayer tubular part for a nuclear reactor comprising a metal layer forming a metal tubular body and two layers of ceramic matrix composite material covering the metal tubular body, wherein one of the two layers in ceramic matrix composite material covers an inner surface of the metal tubular body to form an inner tubular body, whilst the other of the two layers in ceramic matrix material covers an outer surface of the metal tubular body to form an outer tubular body, the metal tubular body therefore being sandwiched between the inner and outer tubular bodies, the metal tubular body having a smaller mean thickness than the mean thicknesses of the inner and outer tubular bodies.