Monte Carlo simulation is increasingly being used in the analysis of large and complex structural systems for the assessment of the uncertainty spread and the reliability. A major handicap for the popularization of this technology is the large number of deterministic evaluations needed to such purposes, inasmuch as linear or nonlinear finite element solvers are required for each output sample calculation. In order to simplify this task neural networks are evaluated in this paper as a partial surrogate of the deterministic solver. The neural networks are trained with the input/output pairs resulting from a few number of finite element simulations, and are henceforth used in a Monte Carlo context. It is shown that when employed in this way, neural networks constitute a promising tool for a drastic reduction of the computational cost needed by a Monte Carlo simulation in this field of application. Three types of networks have been selected for the study, two of which correspond to supervised and the other one to hybrid learning procedures. The paper compares the network designs in their more relevant aspects, which are the training speed and accuracy, the extrapolation ability and the accuracy of the estimated probabilities.