Is SUSY accessible by direct dark matter detection?

We performed a combined analysis of the parameter space of the Minimal Supersymmetric Standard Model (MSSM) taking into account cosmological and accelerator constraints including those from the radiative b\rightarrow s\gamma decay measured by the CLEO collaboration. Special attention is paid to the event rate, R, of direct dark matter neutralino detection. We have found domains of the parameter space with R\simeq 5-10~events/kg/day. This would be within the reach of current dark matter experiments. The b\rightarrow s\gamma data do not essentially reduce these large event rate domains of the MSSM parameter space