Raman spectroscopy offers a method of determining residual stresses in Raman active materials. It can serve as a method to monitor residual stresses in thin film-substrate composites. Measurements of such stresses by the Raman microprobe have been performed on a Si film on quartz and an Al film on quartz. For the quartz, the peak shift of one of the Raman active vibrations due to applied stress was calibrated using strain gauges and the four-point bending method. The measurements of residual strains at the Si/quartz interface using the Raman microprobe were compared to expected residual strains by a model, involving an exponential gradient in the substrate and no gradient in the film. The model shows that a small volume of substrate near the interface about two times the film thickness was affected by the thermal expansion mismatch of the two regions.