The focus of this work is on the elastic response of cubic polycrystals, particularly aluminum alloys, as explored through neutron diffraction with in situ mechanical loading, coupled with elastoplastic finite element simulations. It includes a set of data from experiments, an initial set of finite element simulations of those experiments, an expanded suite of simulations to explore the effects of grain discretization on the results, and a new method of stress estimation from diffraction experiments. Chapter 1 includes an explanation of the methods used along with a presentation of the experimental data referred to throughout the work. It contains the material from [1]. The experiments are neutron diffraction with in situ uniaxial tension loading of aluminum- magnesium alloys of various compositions. The data are reduced with an emphasis on observing elastic anisotropy in the materials. The second and third chapters cover finite element simulation of the experiments. Chap- ter 2 describes the simulation framework along with results from simulations of the exper- iments using dodecahedral grain definitions. The ability of the simulations to capture the elastically anisotropic behavior of the materials is discussed. Chapter 3 expands the set of simulations to include meshes with different grain discretizations. It demonstrates the differ- ent results that are possible with respect to capturing stress variations within a polycrystal aggregate. A method of estimating stresses in various sets of crystals from diffraction experiments based on the yield surface of face-centered cubic single crystals in presented in Chapter 4. The method requires no knowledge of material properties and represents an improvement over an assumption of the macroscopic stress state being identical to that of all crystals. The final chapter is a brief summary of the preceding chapters highlighting the main findings.