A method for obtaining a body (Cp) which must have a given shape, starting with a yarn or the like, characterized by the fact that it consists: • in a first phase, of producing a preform of said yarn in the form of a mixture of fibers and of non-polymerized thermosetting polymerizable resin, linking together said fibers, the fibers being of at least one of the following materials: glass, carbon aramid, • in a second phase, of translating said preform in a first given direction and, during the translation movement (Tr) of the preform, producing a sheath around said preform with a molten sheathing material the melting temperature of which is less than the glass transition temperature of the resin and to the softening temperature of the fibers, said sheathing material being a eutectic material selected among the following mixtures: tin-bismuth, lead-tin-bismuth, • in a third phase, while continuing the translation of the assembly comprising the preform and the molten sheath obtained during the second phase, simultaneously: ∗ cooling said assembly (Ph3-1) using cooling means to obtain a relative solidification of the sheath, and ∗ shaping said assembly (Ph3-2) to obtain said given shape, • in a fourth phase, of maintaining said assembly for a predetermined time at a temperature called the "gelation temperature" to polymerize the resin contained in said preform, • in a fifth phase, of bringing said assembly to a temperature less than the glass transition temperature of the resin but greater than the melting temperature of the sheathing material, until the sheathing has melted completely, the resin then being, at the end of this fifth phase, completely polymerized and post-cured, and • in a sixth phase, of recovering said formed body (Cp). • in a first phase, of producing a preform of said yarn in the form of a mixture of fibers and of non-polymerized thermosetting polymerizable resin, linking together said fibers, the fibers being of at least one of the following materials: glass, carbon aramid, • in a second phase, of translating said preform in a first given direction and, during the translation movement (Tr) of the preform, producing a sheath around said preform with a molten sheathing material the melting temperature of which is less than the glass transition temperature of the resin and to the softening temperature of the fibers, said sheathing material being a eutectic material selected among the following mixtures: tin-bismuth, lead-tin-bismuth, • in a third phase, while continuing the translation of the assembly comprising the preform and the molten sheath obtained during the second phase, simultaneously: ∗ cooling said assembly (Ph3-1) using cooling means to obtain a relative solidification of the sheath, and ∗ shaping said assembly (Ph3-2) to obtain said given shape, ∗ cooling said assembly (Ph3-1) using cooling means to obtain a relative solidification of the sheath, and ∗ shaping said assembly (Ph3-2) to obtain said given shape, • in a fourth phase, of maintaining said assembly for a predetermined time at a temperature called the "gelation temperature" to polymerize the resin contained in said preform, • in a fifth phase, of bringing said assembly to a temperature less than the glass transition temperature of the resin but greater than the melting temperature of the sheathing material, until the sheathing has melted completely, the resin then being, at the end of this fifth phase, completely polymerized and post-cured, and • in a sixth phase, of recovering said formed body (Cp).