Thanks to the materials project, the elastic constants of thousands of compounds are now available, allowing for the screening of all manner of properties. An anomalous material of particular interest is Gum Metal, a class of Ti-Nb alloys that exhibits superelasticity, and high strength. Previous studies have tied the behavior of Gum Metal to a high elastic anisotropy related to the dislocation core radius, which is a direct result of the material’s presence near an elastic instability. By calculating the dislocation core radius of all cubic materials in the elastic constants database Gum Metal candidates are identified. It is shown by incorporating the third-order elastic constants into the elastic stability conditions, the intrinsic ductility of these alloys can be estimated from first principles, presenting an efficient approach for identifying potential high strength, ductile materials. Funding is given by the Department of Energy's Basic Energy Sciences program, grant No. EDCBEE.