In this paper we suggest a new approach to the structure of the soft Pomeron: based on the $t$-channel unitarity, we expressed the exchange of the soft Pomeron through the interaction of the dipole of small size of the order of $1/{Q}_{s}(Y)$ [${Q}_{s}(Y)$ is the saturation momentum] with the hadrons. Therefore, it is shown that the typical distances in soft processes are small $r\ensuremath{\sim}1/{Q}_{s}(\frac{1}{2}Y)$, where $Y=lns$. The saturation momentum, which determines the energy dependence of the scattering amplitude, is proportional to ${Q}_{s}^{2}(\frac{1}{2}Y)\ensuremath{\propto}\mathrm{exp}(\frac{1}{2}\ensuremath{\lambda}Y)$, with $\ensuremath{\lambda}\ensuremath{\approx}0.2$, and this behavior is in perfect agreement with the phenomenological Donnachie-Landshoff Pomeron. We demonstrate that the saturation models could describe the experimental data for ${\ensuremath{\sigma}}_{\mathrm{tot}},{\ensuremath{\sigma}}_{el},{\ensuremath{\sigma}}_{\mathrm{diff}}$ and ${B}_{el}$. Hence, our approach is a good first approximation to start discussion of the soft processes in the color glass condensate approach on the solid theoretical basis.