A sheathed synthetic fiber rope includes concentric layers of load-bearing synthetic fiber strands, preferably of aramide fibers, with an outermost layer of strands having anchoring strands permanently fastened to a sheath extruded onto the outermost layer. The anchoring strands can be formed of weldable or vulcanizable material. Alternatively, a polyurethane jacket surrounding each of the outermost layer strands can be used to permanently fasten the sheath.