The results of numerical study of stress-strain-state (SSS) of a rockfill dam with a face whose main watertight element is a polymer geomembrane. Analyses were conducted with consideration of non-linearity of contact interaction of structure elements and non-linearity of soil behavior. Bar finite elements were used for modelling of the thin geomembrane. The study was conducted on the example of Bovilla dam structural design which was built in 1996 in Albania. Initially Bovilla dam was planned to have a reinforced-concrete face, but later there was realized the design with multy-layered face consisting of PVC geomembrane, the underlying layer of soil-cement and a protection layer of reinforced concrete slabs. The face is conjugated with the concrete structure being an integral part of the dam. The results of numerical analyses showed that the weakest part of the dam design is the place of conjugation of the face with the concrete structure. The joint between the face and the concrete structure opens and the face shifts with relative to concrete surface. The polymer geomembrane may withstand these displacements without damages because the face structural design is provided with a compensating device in the form of a geomembrane loop. However, as calculations showed, the face design provokes formation of tensile stresses in protection reinforced concrete slabs and in the soil-cement underlying layer. In case the dam face was made of reinforced concrete, cracking in the face could be less probable. In our opinion, more feasible solution of the conjugation zone could be the alternative when the polymer geomembrane is placed over the face and is covered by soil protection layer. Taking into account high strength and safety of polymer geomembranes they may be recommended to be used as a backup seepage-control element of high concrete faced rockfill dams.