The results of application of gradient theory of elasticity to a description of elastic properties of dislocations and disclinations are reviewed. The main achievement made in this approach is the elimination of the classical singularities at defect lines and the possibility of describing short-range interactions between them on a nanoscale level. Non-singular solutions for elastic fields and energies of dislocations in an infinite isotropic medium are represented in a closed analitycal form and discussed in detail. Similar solutions for straight disclinations are also considered with application to the specific case of disclination dipoles. A special attention is paid to the nanoscopic behavior and stress fields of dislocations near interfaces. Recent non-singular solutions for both the dislocation stresses and "image" forces on dislocations are demostrated in a general integral form and corresponding peculiarities in dislocation behavior near interfaces are discussed.
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