A unit for grinding biological samples, comprising a grinding device including at least two tubes having different volumes, suitable for being mounted on a support of the grinding device, each tube comprising an inner space having a height (h) along the axis of the corresponding tube, and being intended to contain samples to be ground, means for driving the support in a precession movement, the support having an axis the position of which varies by describing a cone, each tube being subjected to a movement (d) defined by the projection, onto the axis of said cone, of the distance between the extreme positions of a same point of the tube during the precession movement.