A load bearing assembly (100) for use in elevator system wherein the load bearing assembly (100) comprises at least one steel rope (102) and a jacket (110) surrounding this at least one steel rope (102). The jacket (110) comprises at least one layer of a thermoplastic elastomer comprising polymer particles (112). The polymer particles (112) have a molecular weight higher than 0.5*106 g/mol. The jacket (110) provides a coefficient of friction allowing sufficient traction between the load bearing assembly (100) and other components of the elevator system, such as the sheaves. Also disclosed is a corresponding method of making a load bearing member.