I present a Kac-type many particle model that allows a reference-free description of plastic deformation. I calculate an upper bound for the energy barrier of plastic deformations in the model. I demonstrate how finit sequences of regular points can be used to construct local discrete Lagrangian coordinates in the framework of the model. Furthermore, I use discrete coordinates to identify topological defects as dislocations. Finally, I give a lower bound for the energy density in form of a functional of local continous Lagrangian coordinates.