The residual magnetic uniaxial anisotropy of thin films deposited on flexible substrates was studied to elucidate its main origins. For that purpose, we sputtered 20 nm thick films of Co40Fe40B20 and Ni80Fe20 on Kapton R substrates. After measuring magnetomechanical properties of each system, we have shown that the weak residual anisotropy in the Ni80Fe20 film, compared to that of Co40Fe40B20, is perfectly correlated to its low magnetostriction coefficient. As a consequence, we conclude that this residual anisotropy is undoubtedly due to the unavoidable bending of the system, even if it is invisible with the naked eye (radius of several centimeters).