X-ray and ion-beam lithographic processes require the use of advanced masks with free-standing thin membranes. In the fabrication of these masks, the pattern transfer process involves the deposition or removal of a thin layer of material (or portions of a layer), which can produce relatively large pattern placement errors. The stress-induced distortions of both x-ray and stencil mask membranes (due to the individual fabrication processes) have been simulated by finite-element procedures. For patterned areas of both mask membrane types, equivalent models with uniform characteristics have also been developed and assessed for validity. These models facilitate the calculation of global in-plane distortions needed to perform pattern specific emulation.