In the production of fiber reinforced axially symmetrical wound bodies each of predetermined length, by winding fibers or strands of fibers saturated with a hardenable plastic onto a mandrel, alternating layers of circumferential windings and layers with criss-cross windings being placed on top of one another, and, after hardening of the plastic, removing the mandrel, the winding is carried out to simultaneously produce a plurality of identical wound bodies axially juxtaposed on the mandrel by the steps of: winding at least one circumferential layer by attaching a plurality of fibers or strands corresponding to the number of bodies to be wound at axially spaced locations along the mandrel and winding all of the fibers or strands simultaneously on the mandrel with mutual axial spacings approximately corresponding to, or somewhat greater than, the length of each wound body; winding at least one criss-cross winding layer by attaching at least one fiber or strand to the mandrel and winding the fiber or strand over the combined length of the juxtaposed layers of circumferential windings along the mandrel; and dividing the completed wound layers into individual sections forming the respective wound bodies which are then removed from the mandrel.