Abstract: Methods and apparatus are disclosed for accurately measuring stresses in respective membrane regions of segmented mask blanks destined to be made into masks or reticles for use in microlithography. A mask blank is held to a securing plate, e.g., by electrostatic attraction. The mask blank is held such that the struts of the mask blank contact the surface of the securing plate. The securing plate defines an array of through holes that are aligned with individual subfields of the mask blank. A pressure differential is applied across the membrane via the through-holes, causing the membrane regions to bulge. While measuring the pressure, the magnitude of bulge of individual membrane regions is measured using a displacement-measuring device. From data concerning the magnitude of bulge, membrane stress and Young's modulus are determined.