EUV pellicle membranes are being pursued to protect scanner images from repeating defects caused by reticle fall-on particle defects. Because most materials highly absorb EUV, pellicle membranes must be ultrathin. In an attempt to increase the strength of the ultrathin membranes, grid-supported pellicle membranes have been proposed. In this study we compare grid-supported pellicles (GSP) over free-standing pellicles (FSP). We considered imaging, thermal, mechanical, and thermo-mechanical characteristics. Finite Element Methods (FEM) was used to investigate the thermal, and (thermo-)mechanical behavior of pellicles. The maximum temperature reached under operational conditions by the pellicle film was determined. Using a thermo-mechanical analysis wrinkling behavior was quantified. The mechanical analysis considered the influence of grid structures on the sagging behavior, on crack propagation, on the pellicle film resistance to collision with solid particles, and on the resistance to shocks on the pellicle frame. The analysis shows that GSP that meets imaging requirements will not bring any advantages over FSP.