Leptonic decay modes of Z-boson constitute one of the important class of the decays for checking predictions and improving parameters of the standard model. In next generation of the accelerators, it will be produced more than 10^8 Z-boson pear year. Therefore, It appears real possibility to analyze the rare decays of Z, which are absent at tree level in standard model. Moreover, the rare decays are quite sensitive to the existence of new physics beyond the standard model. One of the possible source for the new physics is noncommutative theories (NC). Noncommutative theories have rich phenomenological implications due to the appearance of new interactions, which are forbidden in standard model. In this thesis, we examine the Z $rightarrow nu bar{nu} gamma$ decay in noncommutative standard model. We study the sensitivity of the decay width on the noncommutative scale parameter Lambda and parameters $C_{0i}$ and $C_{ij}$, which defines the direction of background electric and magnetic fields.