Abstract: A method of constructing a liner system for a waste containment facility having substantially vertical sidewalls utilizing a plurality of vertical expansion boxes for holding a flexible membrane liner against a rock face or any other approximately vertical face without penetration of liner, liner "creep", slippage or impairment of the integrity of the liner A vertical expansion box provides lateral and vertical pressure onto portions of the flexible membrane liner to hold it firmly in place. The vertical expansion box is constructed such that when, filled with soil or other aggregate material, lateral pressure of the fill will flex the sidewalls of the box, which in turn applies pressure against the liner.