The machine for tearing beads from the rims of pneumatic tyres comprises a screw-jack traction element (2) whereby the rod thereof is mounted in such a way that it can be displaced in a guided linear manner in a supporting frame receiving the stem of the screw-jack in a fixed position and the free end of said rod is fitted with hooking means (3) extending through a slot (5) in a vertical bearing plate (6) of said frame. The pneumatic tyre is disposed in a vertical position whereby the surface thereof rests against one of the surfaces of the plate, whereby the rim of the tyre cooperates with the hooking means (3) and the slot (5) is made of two asymmetrical cross openings, defining a horizontal opening (5b) and a vertical opening (5a). The horizontal opening is symmetrically disposed on both sides of the vertical opening to enable the bead to be torn off via the horizontal opening when the rod is gradually withdrawn. The invention is characterised in that the plate (6), in combination with the profiled slot, is fitted with two parallelipipedic profiled blocks (7 and 8) which are arranged opposite each other and which are mounted in such a way that they can slide in a guided linear manner in the opposite direction to elastic recall elements in order to be placed in a joined contact position corresponding to temporary closure of the vertical slot (5). The contact surfaces of the blocks (7 and 8) are profiled in such a way that they can be moved apart by introducing the hooking means (3) of the screw-jack (2). Said surfaces have a horizontal slot (7b, 8b) which corresponds with the branches of the horizontal opening (5b) of the slot (5) of the plate (6).