Machining of small holes with arbitrary contours can be performed by focusing a laser beam with a modulated zone plate (MZP). MZP's use the structure of the Fresnel zone plate as the carrier of a modulation function, which contains complete information about the contour to be machined. Spherically corrected MZP's produce aberration-free images within a field angle of 10(-3) rad. It is shown that the background noise due to higher diffraction orders is unimportant under typical machining conditions. A manufacturing procedure for high resolution MZP's with up to 2500 zones etched in chromium or quartz layers deposited on glass substrates is discussed. As in-line holograms have properties similar to MZP's, a simple method of recording wavelength-shift corrected in-line holograms is described. Experiments performed with a stable single-mode Nd(3+)-YAG laser demonstrate that the MZP can be important tool for laser machining purposes.