To analyze the vertical collapse robustness of isolated structures, considering double randomness of structure and seismic wave, a random robustness index was proposed based on the reliability theory. Through analyzing and contrasting the random robustness indexes of different randomness, the influence of randomness on the vertical progressive collapse robustness of isolated structures was revealed. In addition, the influence of PGA on the vertical progressive collapse robustness of isolated structures was studied. And the following results were obtained: The random robustness index can be effectively used for quantitative evaluation of the vertical progressive collapse ability of isolated structures. If only considering random ness of structures or seismic wave, it may overestimate the ability of the structure. The robustness of the isolation structure decreases with the increase of PGA. Under strong seismic, isolation structures are more prone to vertical progressive collapse.