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In the framework of the Standard Model we present new theoretical predictionsfor the branching ratios, double and single differential distributions andforward -- backward leptonic asymmetries for the $\bar B_s \to \mu^+ \mu^- e^+e^-$ decay. In our consideration we take into account the $\phi(1020)$ --resonance contribution; the main contributions of four charmonium resonances :$\psi(3770)$, $\psi(4040)$, $\psi(4160)$ and $\psi(4415)$; $u\bar{u}$ --resonant contribution from $\rho(770)$ and $\omega(782)$; tails contributionsfrom $J/\psi$ and $\psi(2S)$ resonances; non -- resonant contribution of the$b\,\bar{b}$ - pairs, bremsstrahlung and the contribution of the weakannihilation. We provide the prediction for the branching ratio of $\bar B_s\to \mu^+ \mu^- e^+ e^-$ decay with and without the $\phi(1020)$ -- resonancecontribution. We use the model of vector meson dominance (VMD) for calculationof resonances contributions and take into account all substantive terms in$\bar B_s \to \mu^+ \mu^- e^+ e^-$ amplitude that was not considered in thepreviously papers.

Rare decays of the $B_s-$meson into four charged leptons in the framework of the Standard Model