When designing machine equipment, geometrical figures or discontinuities such as notches, holes, steps and curves can occur. Sudden cross-section changes, discontinuities and force flows cause concentrations, particularly in the stress area. Stress concentrations may be formed due to dimensional features of a material or directions of applied forces. Such stress concentrations are considered as they have a notch effect on the material. The notch effect may lead to a breaking and distortion of a material. In this study, a mathematical model estimating the notch-factor values for a grooved round bar in torsion, a round shaft with a transverse hole in torsion and a round shaft with a shoulder fillet in torsion, using artificial neural networks (ANN) is introduced. The model estimates the notch factor using shaft dimensions, torque and corner rounding values. The ANN model developed in the study quickly and accurately estimates the notch-factor values, otherwise obtained from the catalogues with complicated analytical calculations. In this model, the uncertainties occurring in analytical calculations and the calculation errors were eliminated, thus long calculation times were saved as well. The results reviewing the performance of the ANN model developed for a grooved round bar in torsion, a round shaft with a transverse hole in torsion and a round shaft with a shoulder fillet in torsion were quite good. In the study, a multiple regression analysis of the data was also performed, but no conclusion evaluating the data was obtained.