Abstract: A punching or stamping machine for operating on thin material with very high precision comprises a horizontally disposed, elongate fixed base (1) and a hollow movable arm (2) extending parallel to the base and connected to it at one end by a resiliently flexible web (3). At the other end, on machined faces (8 and 9), the arm and the base each carry a set of tools, for example, a set of punches and a corresponding set of dies. The web (3) forms a connection between the arm and the base which will permit the necessary operative movement of the arm in the vertical direction but will not allow significant displacement of the arm relative to the base in a horizontal direction, thus contributing to a maintenance in the accuracy of alignment of the punches and dies which is better than that available with a pivotal connection, which is subject to frictional wear.