A punching device for punching a material, in particular continuous, flat paper and/or cardboard webs, comprising: - a machine rack, - an upper part with at least one punching tool as the male die, - a lower part with at least one punching tool as the female die, wherein the upper part is arranged so as to be linearly movable relative to the machine frame, wherein the lower part is fixedly arranged on the machine frame, wherein an intermediate space is present between the male die and the female die, through which the material to be punched can be guided in a direction perpendicular to a direction of a relative movement between the lower part and upper part, wherein the material to be punched can be stamped by the relative movement between the upper part and lower part as the result of at least one respective punching tool of the upper part engaging with an allocated punching tool of the lower part, wherein each punching tool (5o, 5u) has at least one cutting element (10c, 10d) with at least one respective continuous cutting edge and at least one cutting edge arranged in the upper part interacting with at least one cutting edge arranged in the lower part as the cutting edge and counter-blade, wherein the at least one cutting element (10c, 10d) is detachably connected with the punching tool (5o, 5u), characterized in that at least one centering element is arranged between a cutting element (10a, 10b, 10c, 10d) and a base body of the upper part or of the lower part, wherein the at least one centering element and the cutting element (10a, 10b, 10c, 10d) can be positively and immovably fixed to each other against moving in a direction perpendicular to the direction of the relative movement between the upper part and lower part, while on the other hand can be moved as a composite unit relative to the base body in different directions perpendicular to the direction of the relative movement between the upper part and lower part and in different positions relative to the base body. - a machine rack, - an upper part with at least one punching tool as the male die, - a lower part with at least one punching tool as the female die, wherein the upper part is arranged so as to be linearly movable relative to the machine frame, wherein the lower part is fixedly arranged on the machine frame, wherein an intermediate space is present between the male die and the female die, through which the material to be punched can be guided in a direction perpendicular to a direction of a relative movement between the lower part and upper part, wherein the material to be punched can be stamped by the relative movement between the upper part and lower part as the result of at least one respective punching tool of the upper part engaging with an allocated punching tool of the lower part, wherein each punching tool (5o, 5u) has at least one cutting element (10c, 10d) with at least one respective continuous cutting edge and at least one cutting edge arranged in the upper part interacting with at least one cutting edge arranged in the lower part as the cutting edge and counter-blade, wherein the at least one cutting element (10c, 10d) is detachably connected with the punching tool (5o, 5u), characterized in that at least one centering element is arranged between a cutting element (10a, 10b, 10c, 10d) and a base body of the upper part or of the lower part, wherein the at least one centering element and the cutting element (10a, 10b, 10c, 10d) can be positively and immovably fixed to each other against moving in a direction perpendicular to the direction of the relative movement between the upper part and lower part, while on the other hand can be moved as a composite unit relative to the base body in different directions perpendicular to the direction of the relative movement between the upper part and lower part and in different positions relative to the base body.