<p>The prediction of buckling loads for slender and thin-walled structures under compression loading is important for the structural reliability assessment. The presence of random geometrical imperfections reduces the buckling load and is uncertain. In the framework of a probabilistic buckling analysis, the geometrical imperfections are modeled as correlated random fields and applied on the Finite-Element (FE) model. The buckling analysis is then computed by a Monte Carlo Simulation (MCS). The probabilistic approach in structural engineering demands the assurance of a low probability of failure and thus, high accuracy in the calculation of the probability distribution. The resulting high computational cost of the Monte Carlo Simulation can be reduced with a surrogate model of the FE simulation. The development of an effective surrogate model for random fields is challenging, because of the high dimensional input. In this work, an artificial neural network (ANN) surrogate model is presented, to predict the buckling load of structures considering random fields of geometrical imperfections as input. The training procedure is based on random field and the corresponding buckling load samples obtained from FE simulations. The trained ANN surrogate model is finally applied within a MCS-loop, yielding the probability distribution of the buckling load. Three numerical examples (column, plate and cylindrical shell segment) demonstrate that the ANN is able to learn the input-output relationship for structures with different buckling behaviors. The results are compared with a reference FE solution and the computation time shows, that the presented method is an efficient way to speedup the MCS. It is shown that the ANNs learning ability depends on the correlation length of the random field realizations.</p>