We have developed a new methodology to study the effect of mechanical stress on spin waves in thin films deposited onto compliant substrates. It is based on micro-tensile tests combined with Brillouin light scattering spectroscopy, which allows in situ probing of the magnetization dynamics of the studied film upon deformation. This paper shows from both theoretical and experimental approaches that the magneto-elastic coupling in the saturation regime leads to a simple linear relationship between the spin waves frequency and the stress applied to the magnetic film. The linear part of the experimental data can be reproduced theoretically, assuming a complete strain transfer through the metallic film-compliant substrate interface.