The invention relates to a process for the manufacture of an object, curved in one or more directions, from a package of at least one stacked ply containing polymeric fibers by the deforming thereof at elevated temperature, the process comprising imposing on the fibres a tensile stress at a temperature lying between the melting point of the fibers at the imposed tensile stress and 20° C. below the melting point, which tensile stress is high enough for the fibers to be drawn. This process allows objects, curved in one or more directions, to be produced from flat fiber plies without appreciable wrinkling using even fiber plies with low internal and/or mutual deformability and without material being drawn into the die in a controlled manner. The invention also relates to an object, curved in one or more directions, obtainable by the process according to the invention.