Vertical concrete dry casks, used for interim storage of spent nuclear fuel, are susceptible to large horizontal displacements caused by lateral loads. This study explores the collision between adjacent casks in the case of such large motions. To estimate an upper bound for the probability of failure, a common collision scenario that causes severe structural damage is determined through a comparative deterministic analysis. Then the effects of uncertain parameters on the cask’s performance in the specific collision scenario are studied with a probabilistic approach. Numerical simulations are conducted for 200 realisations of the collision problem to evaluate the canister maximum strain and the overpack accelerations. Then surrogate models, such as polynomial response surface models, multivariate adaptive regression splines, regression trees, and support vector machines, are trained on the response data to derive efficient approximating functions for these responses. Utilising the best developed surrogate models, fragility and the failure probability given collision are estimated. The findings show that the structural integrity of the dry cask is generally maintained in case of the collision. That is, the canister might yield due to the impact loads, but the probability of the canister fracture is negligible for the cask and parameter space considered here.