This paper provides a method for designing anchor benches and trenches used to secure geomembranes exposed to wind action. Only the cases where anchorage is provided by gravity (i.e. by the weight of the material in the bench or trench) are considered. Anchorage by tensile members is not considered. Three potential failure mechanisms are identified for the case of anchor benches: (i) sliding of the anchor bench in the downslope direction (ii) sliding of the anchor bench in the upslope direction and (iii) uplifting of the anchor bench.