The contemporary approach in structural engineering indirectly addresses uncertainties arising from load and resistance parameters by using safety factors. To consider these uncertainties in structural engineering, it is necessary to incorporate their statistical properties into the analysis and design process. However, this approach requires the calculation of challenging multi-fold probability integrals. Approximate methods known as FORM and SORM have been developed as an alternative to calculating those integrals. Unfortunately, these methods might have accuracy and convergence problems depending on the problem at hand. Simulation-based structural reliability methods have been developed to overcome the problems associated with approximate methods. The main problem with these methods is that they are often computationally expensive when along with finite element analysis, or it is hard to implement them when a more specific method is chosen to reduce computational costs. In this study, artificial neural networks have been applied to structural reliability problems to obtain accurate probability estimates with low computational cost. A special type of learning algorithm called Bayesian Regularization was used in the training of artificial neural networks. Additionally, details of the application of artificial neural networks to structural reliability problems are provided. At the end of the study, the advantages and disadvantages of applying artificial neural networks to structural reliability problems are presented and compared with other known structural reliability methods. Additionally, a new convergence criterion and an adaptive algorithm have been developed. It was observed that applying artificial neural networks to structural reliability problems provides both efficient and accurate probability estimates.