An analytical model of the dislocation core is proposed. The center of a crystal dislocation in this model is represented by a continuous distribution of infinitesimal dislocations, whose distribution function incorporates the atomic configurations of dislocations as determined by Cotterill and Doyama using a many‐body‐crystal model of copper. The distribution functions used have the same form as the Peierls model except the width parameter, which is about twice that of the original Peierls model. Using the present model and methods of the continuum theory of dislocations, numerical calculations are made for the interaction energies between two parallel screw and two parallel edge dislocations. The results are significantly different from those predicted by the classical theory when the separation distance is less than ten atomic distances. Approximate expressions for the interaction energy between two coplanar edge dislocations and for that between two coplanar screw dislocations are obtained. The magnitudes of both the interaction energy and interaction force remain finite in the present model, enabling the unique determination of the self‐energies of single dislocations and edge dislocation dipoles. Dislocation splitting in fcc metals is also discussed.