Density functional theory (DFT) calculations show that self-interstitial atom defects in nonmagnetic body-centred cubic (bcc) metals adopt strongly anisotropic configurations, elongated in the h111i direction1–4. Elastic distortions, associated with such anisotropic defect configurations, appear similar to the distortions around small prismatic dislocation loops, although the extent of this similarity has not been quantified. We derive analytical formulae for the dipole tensors of h111i defects in the isotropic and anisotropic elasticity approximations. These expressions show that, in addition to the prismatic dislocation loop-like character, the elastic field of a h111i defect also has a significant isotropic dilatation component. Using a multi-scale approach, which combines DFT calculations with elasticity, we parameterize dipole tensors of defects for all the non-magnetic bcc transition metals. This enables quantitative evaluation of the energy of elastic interaction between the defects, which also shows that in a periodic three-dimensional arrangement, long-range elastic interaction between a defect and all its images favours a h111i orientation of the defect.