Non-local elasticity kernels are calibrated based on the atomic scale structure of glasses obtained from atomistic simulations. A model Morse material, with interatomic interactions described by a pair potential, and Al, characterized by an embedded-atom potential are considered. The study is limited to linear isotropic non-local elasticity. The functional form of the derived kernels is significantly different than that usually assumed in non-local constitutive models (Gaussian). They have a range that extends up to the cut-off radius of the interatomic potential, are positive at the origin, and become negative approximately one atomic distance away. These kernels involve 2 internal length scales that are both derived from atomistics for the materials mentioned above. The kernel for Al is tensorial, a different function weighting each entry of the stiffness tensor. Model materials interacting by pair potentials may be described by a single function that weights the whole stiffness tensor. Two applications are briefly described in closure. The new non-local model improves upon the Gaussian one by predicting a more realistic wave dispersion relationship, with essentially zero group velocity at the boundary of the Brillouin zone. Next, the role of non-locality in defining the Peierls stress of a dislocation is studied within a Peierls-Nabarro model and it is shown that the predictions of the critical stress improve upon consideration of non-locality.