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Body-center-cubic (BCC) magnesium-lithium alloys are a promising light-weight structural material. As a first step in a theoretically guided materials design strategy single crystal elastic coefficients for BCC magnesium-lithium alloys with different compositions were computed using ab initio methods. These single crystal elastic coefficients were then used to predict the corresponding polycrystalline elastic properties using various analytic homogenization techniques (Voigt, Reuss, and a self-consistent approach) as well as the finite element method. As expected, the Voigt and Reuss bounds form the upper and lower bounds on the polycrystalline elastic properties, which the predicted values of the self-consistent approach and finite element approaches fall in between. Additionally, the difference between the polycrystalline elastic properties derived from the self-consistent approach and the finite element method is small illustrating the power and value of the self-consistent approach for non-textured materials.