A collet surface structure is provided for a high-speed hydraulic press having collet interlock in order to eliminate leakage of oil into the clamping region. Furthermore, the formation of a harmful hydrostatic film thickness from the lubricating-oil film between the pressure rods and the collets is prevented, since the oil is immediately forced away due to the high clamping pressure between the clamping faces. These high clamping pressures result from the extremely short space of the lubricating-oil elimination grooves and the large capacity of the grooves. Thus, the oil-eliminating grooves are made large enough to eliminate reliably a hydrostatic oil film of at least 0.1 mm. This regularity is independent of the clamping diameter of the collet.