The continuous development of steel products generates new challenges for the maintenance of manufacturing machines in steel mills. Substantial mechanical stress is inflicted on the machines during the processing of modern high-strength steels. This increases the risks of damage and flaws in the processed material may appear if the capability of a machine is exceeded. Therefore, new approaches are needed to prevent the machine condition from deteriorating. This study introduces an approach to the prediction of mechanical stress inflicted on a roller leveler during the processing of cold steel strips. The relative stress level is indicated by features extracted from an acceleration signal. These features are based on the calculation of generalized norms. Steel strip properties are used as explanatory variables in regression models to predict values for the extracted vibration features. The models tested in this study include multiple linear regression, partial least squares regression and generalized regression neural network. The models were tested using an extensive data set from a roller leveler that is in continuous operation in a steel mill. The prediction accuracy of the best models identified indicates that the relative stress level inflicted by each steel strip could be predicted based on its properties.