The machine for abrasive treatment comprises an abrasive tool (1) and a device for establishing the holding-down force within the machining zone, said device having a housing (3) provided with guideways, wherein poppet sleeves (4) carrying spindles (5) are free to reciprocate so as to translate the holding-down force to the abrasive tool (1), and a feed mechanism (14) located on the housing (3). According to the invention, in the device for establishing the holding-down force the poppet sleeves (4) are interlinked through an elastic member which is regidly coupled to the feed mechanism (14), while the latter mechanism is adapted to damp the travel of the elastic member in the forward and reverse directions of feed. According to an equivalent embodiment of the invention, in the device for establishing the holding-down force the poppet sleeves (4) are interlinked through at least one elastic member (11a) which is regidly coupled to said poppet sleeves, while the feed mechanism (14) is associated with the elastic member (11a) and is adapted to damp the travel of the elastic member (11a) in the forward and reverse directions of feed.