We study the problem of self-interstitials in face-centered- and body-centered-cubic crystals using defect models that include force-constant changes extending up to second neighbors of the defect site. Complete group-theoretic analysis of defect models for the 〈100〉 dumbbell in a fcc lattice and the 〈110〉 dumbbell in a bcc lattice are presented. We apply the results to the calculation of the static-displacement field of 〈100〉-split interstitials in the fcc metals Cu, Ag, Au, Ni, and Al and 〈110〉-split interstitials in the bcc metals Fe, Mo, and W with the use of the Green's-function method of lattice statics. The calculated results for the displacement field, relaxation volume, dipole tensor, and formation energy are compared with those from computer-simulation studies and lattice-statics calculations.