We study structure and electronic states of Cu nanocontacts. The Korringa-Kohn-Rostoker (KKR) Green's function method for low-dimensional systems and the density functional theory in the local density approximation are used in our calculations. Atomic relaxations of nanocontacts and electrodes are performed using ab initio based many body potentials constructed by means of the KKR Green's function method and the tight-binding approach. We demonstrate that nanocontacts exhibit stress oscillations during stretching cuased by changes in their structure. Performing ab initio calculations of electronic states in nanocontacts in a fully relaxed geometry, we reveal a strong enhancement in the density of electronic states at the Fermi level before breaking.