We outline a theory of coexisting elastic and plastic deformations in slidi
ng Charge Density Waves. They occur in the course of the conversion from th
e normal current at the contact to the collective one in the bulk. Several
mechanisms of phase slips via creation and proliferation of dislocations ar
e compared. We present a modeling which helps to interpret space-resolved s
tudies in recent [1] and earlier [2] X-ray experiments, in multi-contact [3
] and optical [4] studies.