Abstract The internal friction (mechanical loss) behavior of dislocations is studied in a model which, for the first time, considers the substitutional solute mobility in the dislocation core to be higher than in the bulk around it. The parameters investigated include the external stress σ xy , the solute concentration c 0, the pinning length of the dislocation and the temperature. It is shown that, at low c 0 and high σ xy , the kinetics of the dislocation motion is determined by the fast diffusion of the solute atoms in the core, while for high c 0 and low σ xy the diffusion of the atoms far away from the dislocation is rate-limiting. The results are compared with the analytical model of Schoeck and are applied to the alloy system SlSi. New experimental results supporting the model are described in a companion paper (Part II).