This paper advanced a finite element method to analyze the stress-strain of the earth dam with vertical or inclined core wall of composite geomembrane by taking earth-rock material· and composite geomembrane as an entity combined with nine new dams of such kind in cold region of northeastern China. Through calculation the stress distribution· of geomembrane in dam body and its position and size of tensile zone wer obtained. As the stress of composite geomembrane caused by displacement of dam body is very small ,it is safe for medium or low head earth-rock dams. The conclusion of which will be of great advantage 1o design and construction. Nine new dams built in northeastern China-have been operated normally for 1-5 years. It is approved that the finite element metllod is reasonable and reliable for dam design.