Abstract
A non‐singular theory of three‐dimensional dislocations is derived from a particular version of Mindlin's anisotropic strain gradient elasticity theory of form II. Using the anisotropic gradient elasticity theory, we give the non‐singular fields produced by arbitrary dislocation loops in anisotropic solids. In particular, we present the anisotropic versions of the Burgers displacement equation with solid angle, the Mura‐Willis equation for the elastic distortion, the Peach‐Koehler stress equation, the Blin equation for the interaction energy and the Peach‐Koehler force.