A method, apparatus and program product monitor a wrap force during a wrap cycle to dynamically control the dispense rate of a packaging material dispenser to meet a desired containment force to be applied to a load. A conversion may be performed between wrap force and containment force for the monitored wrap force or a containment force parameter to facilitate the performance of a comparison between the monitored wrap force and a containment force parameter associated with the desired containment force to be applied to the load. A wrap force parameter may also be dynamically adjusted, and in some instances, the dynamic adjustment may be responsive to monitored wrap force, and may be used to meet a load containment force requirement for a load. In other instances, the dynamic adjustment may be responsive to monitored packaging material breaks to reduce the occurrence of packaging material breaks.