The results of an experimental technique to measure strains using polychromatic X-rays are presented. Using Laue Diffraction, the distribution of strains over an Al-Sapphire fiber composite is studied. An advantage of using polychromatic X-rays, as compared to monochromatic X-rays, is that the diffraction patterns are obtained from nearly all grains as compared to the small fraction observed typically with monochromatic X-rays. The technique proves successful in measuring the residual strains and the strain response to applied stress with an accuracy of 200 micro-strain. Strain maps prove to be helpful in demonstrating the actual grain morphology in 2D and the respective strain states in the form of strain contours for every individual grain. A distribution representative of the nature of residual strains is also obtained at multiple scales with respect to the microstructure. The results, along with the 3D analysis, will help validation and modification of constitutive models for composite failure.