With progressing miniaturization of modern electronic devices, interconnects become increasingly smaller. Additionally, as electronic devices move away from rigid substrates toward flexible ones, understanding their mechanical and structural stability is becoming crucial. In this work, a thorough mechanical characterization of copper thin films deposited on flexible substrates was performed with two techniques, namely well-established synchrotron X-ray diffraction (sXRD) and the rather new usage of reflectance anisotropy spectroscopy (RAS) for mechanical characterization of thin films. The comparison of these two techniques shows that RAS can be reliably used for the accurate and prompt yield stress measurements. The acquisition time of RAS is much faster than that of sXRD: 1 second per data point compared to several seconds per data point for sXRD experiments. Moreover, the signal-to-noise ratio of the RAS data is much higher than that of the sXRD. Our results show that yield stress of Cu films increases with the decrease in the film thickness, going from 352 MPa for a 500 nm films to 793 MPa for a 50 nm thick film. Microstructure analyses of the films by electron microscopy allowed correlation of the mechanical behavior of the films to their grain morphologies. We have shown that RAS can supplement sXRD measurements due to a faster acquisition rate which allowed us to analyze the creep behavior of our copper thin film at different strain rates.