A shear press for scrap comprising a machine body defining a compaction channel adapted to contain the scrap and guide it in a sliding manner along a predetermined advance direction, compaction means adapted to compact the scrap into the compaction channel, and cutting means positioned at one axial end of the compaction channel to separate the compacted scrap into portions, wherein the compaction means comprise: - two mutually opposed jaws articulated to the machine body according to axes of rotation parallel to each other and orthogonal to the advance direction of the scrap, and - actuating members adapted to rotate said jaws around the respective axes of rotation, in opposite directions, between an open configuration and a closed configuration, thereby reducing the space between the two jaws, wherein each jaw comprises an operating surface adapted to laterally delimit the compaction channel when the jaw is in the open configuration, and wherein the cross section of said operating surface, carried out with respect to a section plane orthogonal to the axis of rotation, comprises an end proximal to the axis of rotation, an end distal from the axis of rotation and at least one first rectilinear stretch that is parallel to the advance direction of the scrap when the jaw is in the closed configuration, wherein the cross section of the operating surface comprises a further rectilinear stretch that extends from the first rectilinear stretch to the proximal end of the cross section of the operating surface, characterized in that the extreme point of said first rectilinear stretch with respect to the axis of rotation of the jaw does not coincide with the distal end of the cross section of the operating surface but is aligned to the latter along a direction of alignment which forms, with said first rectilinear stretch, an angle (α) having its vertex facing the inner part of the compaction channel. wherein the compaction means comprise: - two mutually opposed jaws articulated to the machine body according to axes of rotation parallel to each other and orthogonal to the advance direction of the scrap, and - actuating members adapted to rotate said jaws around the respective axes of rotation, in opposite directions, between an open configuration and a closed configuration, thereby reducing the space between the two jaws, - two mutually opposed jaws articulated to the machine body according to axes of rotation parallel to each other and orthogonal to the advance direction of the scrap, and - actuating members adapted to rotate said jaws around the respective axes of rotation, in opposite directions, between an open configuration and a closed configuration, thereby reducing the space between the two jaws, wherein each jaw comprises an operating surface adapted to laterally delimit the compaction channel when the jaw is in the open configuration, and wherein the cross section of said operating surface, carried out with respect to a section plane orthogonal to the axis of rotation, comprises an end proximal to the axis of rotation, an end distal from the axis of rotation and at least one first rectilinear stretch that is parallel to the advance direction of the scrap when the jaw is in the closed configuration, wherein the cross section of the operating surface comprises a further rectilinear stretch that extends from the first rectilinear stretch to the proximal end of the cross section of the operating surface, characterized in that the extreme point of said first rectilinear stretch with respect to the axis of rotation of the jaw does not coincide with the distal end of the cross section of the operating surface but is aligned to the latter along a direction of alignment which forms, with said first rectilinear stretch, an angle (α) having its vertex facing the inner part of the compaction channel.