A method is provided for a rotary press of the type including at least one cylinder for printing and feeding a web to be printed, and a device for driving in rotation the or each printing and feed cylinder.In normal operation, the at least one cylinder is driven by applying thereto a positive drive torque and a positive drive power, and, in the event of the web breaking, the at least one cylinder is braked by the associated drive device.According to one embodiment of the invention, in an emergency shutdown step, the torque or the power applied to the at least one printing and feed cylinder by the associated drive device is limited in such a manner as not to exceed a predetermined torque threshold or power threshold.