The material is in a fluid state at a predetermined temperature above the ambient temperature. According to the invention: a) at least two different compositions of this material in the fluid state are prepared; b) simultaneously and concentrically both the core of the rod with the aid of one of the compositions and a sheath enveloping this core with the aid of another composition are cast; and c) the casting is then taken to a temperature at which it solidifies to constitute the rod. Advantageously, the section of the casting is made to grow by its passing through a cylindrical mold shaped to define the final section of the rod. Application to the manufacture of a glass rod presenting a cross-sectional refractive index gradient.