Method to control the vibrations of an articulated arm (11) during its movement and use to carry out pumping operations of concrete, the articulated arm comprising a plurality of segments (12) articulated with respect to each other, each associated with a corresponding actuator (13).The method comprises at least a first step of detecting the temporal development and entity of the force which acts on at least said actuator (13) due to the vibrations, and a second step during which a processing and control device (31), as a function of said force, commands the drive of a hydraulic control circuit (30) connected fluidically at least to the actuator (13) to determine the damping of said force due to the vibrations.