Manufacturing parts made of thin steel in small batches is a challenging task in terms of reaching the proper balance between the productivity, the cost, and the dimensional precision. This paper presents the results of experimental research about manufacturing electrical steel thin parts using abrasive waterjet cutting. For a certain increase of productivity and a more efficient process, the parts were cut using multilayer packages of steel strips. The main objective was to analyze the influence of the number of layers on the dimensional precision of parts. Preliminary tests were performed, followed by a full factorial experiment using two independent parameters, the number of layers and the traverse speed. The parts were measured on a noncontact vision measurement machine and mathematical models were determined to predict the parts deviations depending on the independent parameters used. A practical validation of the models was performed. The main conclusion is that the number of layers has a certain influence on the accuracy of dimensions, but this influence can be predicted with a satisfactory level of confidence using mathematical models.