The failure of balloons made of Linear Low Density PolyEthylene (LLDPE) is investigated. The chosen film is 38 µm thick StratoFilm 420, currently used for the NASA Super-Pressure balloons [1]. The visco-elastic behaviour of the film has been extensively studied and is already accounted for in the balloon design [2, 3, 5]. The next step in the development of accurate predictive tools for super-pressure balloons requires models that capture the transition from visco-elastic and visco-plastic behaviour to fracture. It is shown that realistic estimates of failure of LLDPE membrane structures can be obtained from visco-elastic simulations based on the non-linear visco-elastic model of the balloon film proposed by Kwok [5], supplemented with a fracture resistance criterion derived from the experimentally-based J-integral.