Hybrid rope (20) comprising a core element (22) containing high modulus fibers surrounded by at least one outer layer (24) containing wirelike metallic members (26). The core element (22) is coated (23) with a thermoplastic polyurethane or a copolyester elastomer, preferably the copolyester elastomer containing soft blocks in the range of 10 to 70 wt %. The coated material (23) on the inner core element (22) is inhibited to be pressed out in-between the wirelike members (26) of the hybrid rope (20) and the hybrid rope (20) has decreased elongation and diameter reduction after being in use.