In many biological processes, e.g. the fermentation of cells and sensitive microorganisms or bioconversion with immobilised enzymes, low shear stress is of crucial importance for the optimal course of processes. Starting with the causes of particle stress, the following report discussed the hydrodynamic principles of the most frequently used model reactors and bioreactors, which are required for an approximate calculation of stress. The main part of the report describes the results of systematic investigations into the hydrodynamic stress on particles in stirred tanks, reactors with dominating boundary-layer flow, shake flasks, viscosimeters, bubble columns and gas-operated loop reactors. These results for model and biological particle systems permit fundamental conclusions on particle stress and the dimensions and selection of suitable bioreactors according to the criterion of particle stress.