An elevator rope (100) comprises a steel cord (114) and an elastomer jacket (140) surrounding the steel cord. One or more yarns (120, 122) are wrapped or braided or knitted around the steel cord before the elastomer jacket is applied. The yarns are therefore integrated into the polymer jacket. The yarns induce a pattern at the surface of the polymer jacket. By amending the yarn structure, the surface pattern of the polymer jacket can be changed. This has an implication on the friction of the elevator rope on the sheave on which it is running. Furthermore, the integrated yarns help to preserve the integrity of the elastomer jacket. In a second aspect of the invention a method is claimed wherein first one or more yarns are wrapped, braided or knitted around the steel cord prior to extrusion of the elastomer. The yarn mantle ensures a good centricity of the elastomer jacket and an improved processability of the elevator rope.