Fixtures are an important element of the manufacturing system, as they ensure productive and accurate machining of differently shaped workpieces. Regarding the fixture design or the layout of fixture elements, a high static and dynamic stiffness of fixtures is therefore required to ensure the defined position and orientation of workpieces under process loads, e.g. cutting forces. Nowadays, with the increase in computing performance and the development of new algorithms, machine learning (ML) offers an appropriate possibility to use regression methods for creating realistic, rapid and reliable equivalent ML models instead of simulations based on the finite element method (FEM). This research work introduces a novel method that allows an optimization of clamping concepts and fixture design by means of ML, in order to reduce manufacturing errors and to obtain an increased stiffness of fixtures and machining accuracy. This paper describes the preparation of a dataset for training ML models, the systematic selection of the most promising regression algorithm based on relevant criteria, the implementation of the chosen algorithm Extreme Gradient Boosting (XGBoost) and other comparable algorithms, the analysis of their regression results, and the validation of the optimization for a selected clamping concept.