The Method of Auxiliary Sources (MAS) is efficiently used in the synthesis problem of antenna with the given far field pattern, by means of the radiated field's fundamental singularities determination. The paper is the continuation and the generalization to the 3D cases our previous publications. As it is known, the same directivity pattern, at the given frequency, could be obtained with the different current distribution on different antenna surface. The problem is reduced to the finding of the more or less optimal current distribution, which is unique. This means the minimal values of the: currents, reactive near field values and also the best matching between antenna and radiation. In the given work is confirmed that the optimal currents' distribution is related to the fundamental singularities of the radiated field.