A shock-absorbing hitch termination (40) includes a terminating member (52) that moves against a first bias (62) responsive to a first level of tension on a load bearing member (26) associated with a car (22) and counterweight (24) in an elevator system (20). A support member (60) moves with the terminating members (52) against a second, passive bias (70) responsive to increased tension on the load bearing member (26). In one example, the second bias is provided by mechanical springs (70). In another example the second bias is provided by air springs. In still another example the second bias is provided by pressurized actuators (82). The shock-absorbing hitch termination may be supported for movement with the car, counterweight or both. In another example, the shock-absorbing hitch termination is provided in a stationary structure (90) within the elevator system.