Possible constraints on SUSY-model Parameters from Direct Dark Matter Search

We consider the SUSY-model neutralino as a dominant Dark Matter particle in the galactic halo and investigate some general issues of direct DM searches via elastic neutralino-nucleus scattering. On the basis of conventional assumptions about the nuclear and nucleon structure, without referring to a specific SUSY-model, we prove that it is impossible in principle to extract more than three constraints on fundamental SUSY-model parameters from the direct Dark matter searches. Three types of Dark matter detectors probing different groups of parameters are recognized.