Residual stress of case-hardened steel samples is predicted in this paper with the linear multivariable regression model. The development of the prediction model is based on the huge set of features calculated from the Barkhausen noise measurement signal among which the most suitable ones are chosen. The selection uses a genetic algorithm with leave-multiple-out cross-validation in the objective function. The original feature set contains collinear features that make the selection task even more complex. Thus a feature elimination procedure based on the successive projections algorithm is studied in this paper. Also the standard genetic algorithm is slightly modified to better serve the feature selection task. The obtained results are good showing that the proposed procedures suit well for residual stress predictions. Also the applied feature elimination procedure is applicable and can be safely used to reduce the dimensionality of the selection problem.