An elevator installation wherein damage to a support for an elevator car and a counterweight, in particular damage to a sheath of the support, advantageously can be detected. At the elevator installation, a housing at least partially extending around the support, for example at a deflecting roller arrangement. A surface of the housing facing the support is electrically conductive and is electrically grounded. If the support or a wire coming out of the damaged support comes in contact with the housing, an electrical ground fault results. The ground fault can be detected by a security monitoring unit by monitoring a current flowing through the wires of the support, and the damage to the support can thus be inferred.