Geomembranes play an important role in the liner system of landfills, where the interfacial strength between rough geomembranes (GM) and nonwoven geotextiles (GT) is low and prone to landslides. There are highly uneven and randomly distributed asperities distributed on the surface of the rough geomembrane, and the mesomechanical properties of the asperity determine the interfacial strength of GMX/GT. A modified large direct shear apparatus was used to conduct uniaxial compression tests on the GMX/GT interface, and the contour height of the geomembrane surface before and after compression was measured using a profiler. By simplifying the contact model of GMX/GT, the normal deformation law of a rough surface asperity with gradually increasing normal load was studied. By comparing the theoretical and experimental results, the deformation process of the asperity on the surface of the geomembrane is clarified, and the normal deformation mechanism of the rough geomembrane is revealed from a microscopic perspective