This thesis deals with the development and testing of an industrially suitable, robust and costefficient measurement setup for carrying out residual stress measurements with surface acoustic waves. In the beginning, the necessary theoretical background on residual stresses, the acoustoelastic effect and sound waves in solids is explained. The relationship between mechanical stress and acoustic waves in solid materials has been known for a long time, but the research results are inconsistent. Stress induced changes of the wave velocity are in a range of around 0.002 %/MPa, which is why the measuring system must be very precise. The sampling rate of the analog-to-digital converter and the measuring distance required to measure these velocity changes are calculated. Furthermore, the influences of various factors that affect time of flight measurement such as signal shape, dispersion, roughness and temperature are illustrated with examples from literature and own results. The necessary measuring devices such as transducers, laser vibrometer, oscilloscope and laser ultrasound equipment are then explained and the differences between the individual measurement methods were outlined. Afterwards, verification experiments are done with piezoelectric surface actuators that are glued to a 25CrMo4 sample. In various tests, the sample was subjected to tensile and bending stresses and the resulting change of wave velocity was determined by measuring the time of flight. The results were able to prove the acoustoelastic effect, i.e. the stress-dependent change of wave velocity. This means that in the future this simple measurement setup can be used to detect changes in residual stress during maintenance.