The angle of seismic excitation is a significant factor of the seismic response of RC buildings. The procedure required for the calculation of the angle for which the potential seismic damage is maximized (critical angle) contains multiple nonlinear time history analyses using in each one of them different angles of incidence. Moreover, the seismic codes recommend the application of more than one accelerograms for the evaluation of seismic response. Thus, the whole procedure becomes time consuming. Herein, a method to reduce the time required for the estimation of the critical angle based on Multilayered Feedforward Perceptron Neural Networks is proposed. The basic idea is the detection of cases in which the critical angle increases the class of seismic damage compared to the class which arises from the application of the seismic motion along the buildings’ structural axes. To this end, the problem is expressed and solved as Pattern Recognition problem. As inputs of networks the ratios of seismic parameters’ values along the two horizontal seismic records' components, as well as appropriately chosen structural parameters, were used. The results of analyses show that the neural networks can reliably detect the cases in which the calculation of the critical angle is essential.