abstract: n this talk, we are interested in the collective behaviour of linear defects in crystal, called dislocations, when the number of dislocations goes to infinity. We will study a simple model for such a dynamics and we will present an homogenization result in its simplest form. The goal is to pass from the dynamics of several dislocation lines to the dynamics of dislocation density. We will also give some qualitative properties of the effective hamiltonian. This is a joint work with Cyril Imbert and Régis Monneau.