A tensioning wedge device for fastening tools to machine tools, in particular dies in forging hammers or presses, comprising - a wedge element with at least one inclined wedge surface and an end surface, the element having a passage bore extending between the front surface and the at least one wedge surface, - at least one counter wedge element with an inclined counter wedge surface for abutment against the at least one wedge surface of the wedge element, as well as with an end face and a passage bore extending between the front surface and the counter wedge surface, - a tensioning bolt extending through the passage bores (52, 54) of the wedge element and the at least one counter wedge element, the bolt comprising a tensioning bolt head, as well as a tensioning bolt shaft with an external thread end opposite the tensioning bolt head, and a tensioning bolt nut for threaded engagement with the external thread end of the tensioning bolt shaft, - wherein the tensioning bolt head, the tensioning bolt nut and/or the external thread end of the tensioning bolt shaft protrude at least partly from the end surfaces (40, 42) of the wedge element and the at least one counter wedge element (36, 38), - a plate spring package surrounding the tensioning bolt shaft of the tensioning bolt between the tensioning bolt head thereof and the end surface of the wedge element or the at least one counter wedge element (36, 38) facing the tensioning bolt head, which package comprises a plurality of plate spring rings having a material thickness and - seen in the relaxed state - and axial height, and which package is adapted to be compressed by a spring deflection predefined in dependence on the degree of pretension, - wherein the passage bore (52, 54) of the wedge element or of the at least one counter wedge element is substantially cylindrical in a first bore section that ends at the end surface (40, 42) of the wedge element (36, 38) or the at least one counter wedge element, which faces the tensioning bolt head, and wherein a second, tapered conical bore section adjoins this first bore section, and - wherein the tensioning bolt shaft has a first, substantially cylindrically shaped shaft section which extends through the first bore section of the passage bore and wherein a second, tapered conical shaft section adjoins this first cylindrical shaft section of the tensioning bolt shaft, characterized in - that, with the tensioning bolt shaft in the passage bore (52, 54), the conical shaft section thereof has a minimum distance from the conical bore section of the passage bore (52, 54) that is at least equal to the predefined spring deflection of the plate spring package plus at least 0.3 and at most 0.8 times the spring deflection. - a wedge element with at least one inclined wedge surface and an end surface, the element having a passage bore extending between the front surface and the at least one wedge surface, - at least one counter wedge element with an inclined counter wedge surface for abutment against the at least one wedge surface of the wedge element, as well as with an end face and a passage bore extending between the front surface and the counter wedge surface, - a tensioning bolt extending through the passage bores (52, 54) of the wedge element and the at least one counter wedge element, the bolt comprising a tensioning bolt head, as well as a tensioning bolt shaft with an external thread end opposite the tensioning bolt head, and a tensioning bolt nut for threaded engagement with the external thread end of the tensioning bolt shaft, - wherein the tensioning bolt head, the tensioning bolt nut and/or the external thread end of the tensioning bolt shaft protrude at least partly from the end surfaces (40, 42) of the wedge element and the at least one counter wedge element (36, 38), - a plate spring package surrounding the tensioning bolt shaft of the tensioning bolt between the tensioning bolt head thereof and the end surface of the wedge element or the at least one counter wedge element (36, 38) facing the tensioning bolt head, which package comprises a plurality of plate spring rings having a material thickness and - seen in the relaxed state - and axial height, and which package is adapted to be compressed by a spring deflection predefined in dependence on the degree of pretension, - wherein the passage bore (52, 54) of the wedge element or of the at least one counter wedge element is substantially cylindrical in a first bore section that ends at the end surface (40, 42) of the wedge element (36, 38) or the at least one counter wedge element, which faces the tensioning bolt head, and wherein a second, tapered conical bore section adjoins this first bore section, and - wherein the tensioning bolt shaft has a first, substantially cylindrically shaped shaft section which extends through the first bore section of the passage bore and wherein a second, tapered conical shaft section adjoins this first cylindrical shaft section of the tensioning bolt shaft, characterized in - that, with the tensioning bolt shaft in the passage bore (52, 54), the conical shaft section thereof has a minimum distance from the conical bore section of the passage bore (52, 54) that is at least equal to the predefined spring deflection of the plate spring package plus at least 0.3 and at most 0.8 times the spring deflection.