A device comprising cyclic plates driven by flexible blades for controlling a helicopter rotor. The device comprises upper flexible curved blades pivotably mounted on the rotor shaft, above the rotary plate, and pivotably mounted by a ball joint on the rotary plate, so as to cause it to rotate with the rotor shaft and at least one lower flexible curved blade, pivoting on an element of the structure of the helicopter and pivotably mounted by a ball joint on the non rotary plate, so as to secure it against rotation. The transverse stiffness of the blades ensures centering of the plates whereas the longitudinal flexibility of the blades and their end pivot point allow the blades to follow the axial translational and tilting movements imparted to the plates by pilot controls pivotably mounted to the non rotary plate, and transmitted to levers controlling the angle of attack of the rotor blades by means of links pivotably mounted to the rotary plate.