The paper presents the results of a series of numerical research on the possibility of applying Artificial Neural Networks (ANNs) for ultimate strength calculations of selected parts of rotating machines. The layout and the principle of the algorithm operation were described, beginning from the general assumptions and then moving to the detailed description of the subsequent modules. The effects of applying the algorithm were presented on the example of the analysis of the compressor disc. The significant benefits of using it were the reduction of optimization time by about 40% and the disc weight reduction by 0.5 kg. Accuracy of ANNs was different in each iteration of a presented algorithm. Finally, high accuracy of neural networks was achieved with the following mean values of relevant indices reached in the last iteration: RMSE=0.5983, MAPA=0.0733 and R^2=0.99895. The further perspectives of undertaken research were defined at the end.