Geomembrane installed on the bottom and the side slope of a waste landfill as liner system is made of high density polyethylene or thermo plastic elastmer polyplopylene. Stress in the geotextile is caused by friction between the waste and the geotextile which is a result of the compression of the disposed waste, and the tensile force is transferred into the liner system by friction. With elapsed time, the stress relaxation will occur under certain strain conditions. If the stress of geomembrane is at high stress for a long period of time, the long time design strength of the geomembrane may be controlled by the creep at the end of the design life. So it is very important for design to determine the stress induced in the geomembrane. In this paper, the authors present a formula based three element visco-elastic model to evaluate the relation between the stress and elapsed time. Then the authors present some results of modeled tests conducted, it is shown that the relation between the material characteristic and temperature by indoor experiment.