The measurement of residual stresses by the hole-drilling method has been used to evaluate residual stresses in structural members. In this method, eccentricity can usually occur between the hole center and rosette gage center. In this study, we obtained the magnitude of the error due to eccentricity of a hole through the finite element analysis. To predict the magnitude of the error due to eccentricity of a hole in the biaxial residual stress field, it could be learned through the back propagation neural network. The prediction results of the error using the trained neural network showed good agreement with FE analyzed results.