Actuation system for a canvas (22) for covering containers (11) of vehicles or containers for excavation waste, the canvas (22) being hauled by one or more cable loops (18) made to move by drive pulleys (16) that transfer to them the motion necessary to move the canvas (22). The actuation system is characterised in that it comprises a support structure (12) arranged on top of the container and comprises transmission means (21, 32, 42) to transmit a rotary driving force to the drive pulleys (16).