Membrane-based photomask is used in proximity X-ray lithography including that in LIGA (Lithographie, Galvanoformung und Abformung) process, and near-field photolithography. In this article, out-of-plane deformation (OPD) and in-plane displacement (IPD) of membrane-based photomask blanks are theoretically analyzed to obtain the mask blanks with flat front surface and low stress absorber film. First, we derived the equations of OPD and IPD for the processing steps of membrane-based photomask such as film deposition, back-etching and bonding, using a theory of symmetrical bending of circular plates with a coaxial circular hole and that of deformation of cylinder under hydrostatic pressure. The validity of the equations was proved by comparing the calculation results with experimental ones. Using these equations, we investigated the relation between the geometry of the mask blanks and the distortions generally, and gave the criterion to attain the flat front surface. Moreover, the absorber stress-bias required to obtain zero-stress on finished mask blanks was also calculated and it has been found that only little stress-bias was required for adequate hole size of support plate.