Using solitonic solution generating techniques we constructed an exact stationary asymptotically flat 5-dimensional vacuum solution describing "black di-ring": concentric black rings rotating on the same plane. There are two different solution generating techniques. First a solitonic method based on the Neugebauer's Backlund trnsformation was applied to construct the black di-ring solution. After the above attempt the Belinsky and Zakharov's inverse scattering method was used to generate the black di-ring. The representations of these two solutions are very different. It was shown that these two solution sets of black di-rings are completely equivalent. One of the most important feature of black di-ring is continuous non-uniqueness. This fact can be confirmed by a random systematical sampling in the phase diagram. It was shown that black di-rings can realize states of thermodynamical equilibrium where the both rings have same temperatures and same angular momenta.