The oxide known as LLZO, with nominal composition Li7La3Zr2O12, is a promising solid electrolyte for Li-based batteries due to its high Li ion conductivity and chemical stability with respect to lithium. Solid electrolytes may also enable the use of metallic Li anodes by serving as a physical barrier that suppresses dendrite initiation and propagation during cycling. Prior linear elasticity models of the Li electrode/solid electrolyte interface suggest that the stability of this interface is highly dependent on the elastic properties of the solid separator. For example, dendritic suppression is predicted to be enhanced as the electrolyte’s shear modulus increases. In the present study a combination of first-principles calculations, acoustic impulse excitation measurements, and nanoindentation experiments are used to determine the elastic constants and moduli for high-conductivity LLZO compositions based on Al and Ta-doping. The calculated and measured isotropic shear modulus are in good agreement, and fall within the range of 56 to 61 GPa. These values are an order of magnitude larger than for Li metal, and far exceed the minimum value (~8.5 GPa) believed to be necessary to suppress dendrite initiation. These data suggest that LLZO exhibits sufficient stiffness to warrant addi-tional development as a solid electrolyte for Li batteries.