An elevator system with a car or platform to transport passengers and/or goods as well as with a counterweight, which are arranged as traversable or movable along a travel path, and which are coupled and/or with a drive by a suspension element interrelating their motion. The suspension element is guided and/or driven by a traction sheave and/or a drive shaft and/or a deflecting pulley. The suspension element is sheathed and/or belt-type, with a first layer made of a first plasticizable and/or elastomeric material, containing a first exterior surface, and with at least one tension member—rope-type, tissue-type, or comprising a multitude of partial elements—that is embedded in the first layer of the suspension element. A manufacturing procedure for one of the suspension elements is provided.