The prediction of spall response of reinforced concrete members like columns and slabs have been attempted by earlier researchers with analytical solutions, as well as with empirical models developed from data generated from physical or numerical experiments, with different degrees of success. In this article, compared to the empirical models, more versatile and accurate models are developed based on model-free approach of artificial neural network (ANN). Synthetic data extracted from the results of numerical experiments from literature have been utilized for the purpose of training and testing of the ANN models. For two concrete members, namely, slabs and columns, different sets of ANN models were developed, each of which proved to have definite advantages over the corresponding empirical model reported in literature. In case of slabs, for all three categories of spall, the ANN model results were superior to the empirical models as evaluated by the various performance metrics, such as correlation, root mean square error, mean absolute error, maximum overestimation and maximum underestimation. The ANN models for each category of column spall could handle three variables together: namely, depth, spacing of longitudinal and transverse reinforcement, as contrasted to the empirical models that handled one variable at a time, and at the same time yielded comparable performance. The application of the ANN models for spall prediction of concrete slabs and columns developed in this study has been discussed along with their limitations.