A tool system for mounting an elastic sleeve includes a holdout tube supporting the elastic sleeve prior to and during mounting, the holdout tube having a longitudinal axis, an interface element movable along the longitudinal axis and transferring pressure onto the elastic sleeve to push the elastic sleeve off the holdout tube during mounting, and an actuation lever engaging the holdout tube at a fulcrum region of the actuation lever. The actuation lever has a pair of load arms partly encompassing the holdout tube. A load region is arranged at a peripheral end of each of the load arms. The actuation lever actuates the interface element by pressing the load regions of the actuation lever against the interface element.