This relates to a method, a device and a curved molded member made of composite material. From at least one composite strip (24) formed of at least two tapes (3, 4, 5) made of unidirectional reinforcing fibers, pre-impregnated with resin and pre-compacted one with the other, the strip is applied longitudinally on a silicone flexible mandrel (13), by compaction under vacuum to confer the specific shape of the mandrel to it, the resulting strip (24) is deposited on a heated metal tool (31) having a curve that complements the shape of the mandrel and forming the core (32) of a pressure and temperature application mold (26), the flexible mandrel is removed then the mold is brought to pressure and temperature for polymerization, and the member is demolded after cooling.