Liquid thin films have long been studied in the context of industrial, biological and geophysical applications from spin coating in microcircuit fabrication to the liquid lining in the lung. For thin film flow, a lubrication approximation simplifies the bulk flow dynamics to a single equation, relating the depth-averaged horizontal fluid velocity to the shape of the gas-liquid interface. In general, these equations are regularized by surface tension which arises as a fourth order diffusive term. However, if the film is bounded by a flexible membrane, elastic effects take on the role of surface tension and the resulting depth-averaged equation becomes sixth order rather than fourth. We discuss some of the consequences of this variation in the context of several commonly observed phenomena from sliding paper to crawling snails.