A neural network approach to theoretical prediction of required residual stresses is considered here. Artificial neural networks trained well and long enough on residual stresses induced by various contact loads may provide very fast response. Results of numerical meshless finite difference analyses were pre- processed and introduced into the neural networks as input and output parameters. The study was performed for two different types of neural networks: a backpropagation neural network (BPNN) and a newly examined radial basis function neural network (RBF).