A model of the process of magnetron sputtering that allows the prediction of the composition of the films deposited using sputtering of mosaic targets with the arbitrary location of the inserts for axial mag netron sputtering systems (MSS) is proposed. The model is based on the integration of the sputtered flows from each point of the sputtering zone, and it takes into account the sputtering yields and the electron ion emission of the material of the base and inserts. The curve of the distribution of the discharge current density is approximated using the third central moment in the double Gaussian distribution, which makes it possible to use real parameters of the sputtering zone and the discharge current of the magnetron. This allows the fairly accurate mathematical description of the distribution of the ion current density. To verify the proposed model, experimental studies on depositing thin film using magnetron sputtering of Ti/Zr and Ti/Zr/Pb mosaic targets were carried out. The model’s error does not exeed 10%.