Ab initio density functional theory molecular dynamics extensive calculations were used for the first time to evaluate stability conditions for relevant phases of InN. In particular, thermal decomposition of InN with formation of N2 molecules and pressure induced wurtzite – rocksalt solid-solid phase transition were established. The results consistent with available experimental data allowed a critical evaluation of potential and limitations of the proposed simulation method. The ab initio molecular dynamics as an efficient tool for simulations of phase transformations of InN including solid-solid structural transition and thermal decomposition with formation of N2 molecules has been demonstrated. It is of high interest because InN being important component of epitaxial quantum structures has still not been obtained as a bulk single crystal making difficult a determination of its basic physical properties and designing new applications.