An optical fiber cable includes a flexible pipe of a plastics material, and a group of optical fibers loosely mounted within an axial bore of the pipe and held in contact with an inner surface of a peripheral wall of the pipe. At least one elongated flexible reinforcing member is embedded in the peripheral wall of the pipe and extends along a longitudinal axis of the cable, the reinforcing member being disposed in the vicinity of the group of optical fibers and made of a material having a higher Young's modulus than that of the plastics material of which the pipe is made. The optical fiber cable has a neutral axis extending through the bore of the pipe and defining a line of zero stress when the cable is bent longitudinally in a direction to dispose the reinforcing member radially inwardly of the group of optical fibers. The group of optical fibers are disposed on the neutral axis, so that the optical fibers are not subjected to axial contraction or elongation when the cable is bent in the direction.