We consider kinematics of a defective medium in terms of Riemann-Cartan geometry supposing nonholonomic transformation. Torsion tension is identified with dislocation density. For incompatible transformation the connection and metric tensor is modified in order to describe the new state of the current medium.

At each point of the body B , a local frame is attached. A priori transformations of the frames and material points behave independently. In our approach, the difference between them, the creation of defects in the current configuration. In practice, there exist two independent Mechanisms, the first mechanism is the ordinary dragging of the vectors of the deformation of the gradient of the macro or the transformation of the point \ Phi, repressed by the tensor with entries F_{A} ^{a} = \ partial_{A} \ Phi ^{a}.The second mechanism is the one associated with the \ Psi transformation of the microstructure characterized by the frame.

Each configuration is definition by its torsion and curvature. The relationship between reference and current curvature is expressed by the action of \ Psi. By point of view, there are two types of strains, the first one measures the changes length and the angles of the material point. The last one associate with the modification of the local frames. Accordingly, an energy function can be obtained in the form \ Xi = \ Xi_ {\ Phi} + \ Xi_ {\ Psi}, where \ Xi_ {\ Phi} ; \ Xi_ {\ Psi} be the macroscopic energy and the microscopic energy, respectively. The relationship with the Kroner decomposition F = F_ {e} F_ {p} will be presented.