In seismic analyses of structures, additional eccentricity is introduced to take account for oscillations of random and unknown origins. In many codes of practice, the torsion about the vertical axis is considered through empirical accidental eccentricity formulation. Due to the random nature of structural systems, it is very difficult to evaluate the accidental eccentricity in a deterministic way and to specify its effect on the overall seismic response of structures. The aim of this study is to develop a procedure for the evaluation of the accidental eccentricity induced by uncertainties in stiffness and mass of structural members, using the neural network techniques coupled with Monte Carlo simulations. This method gives very interesting results for single story structures. For real structures, this method can be used as a tool to determine the accidental eccentricity in the seismic vulnerability studies of buildings.