Rare decays at LHCb

Rare loop-induced decays are sensitive to New Physics in many Standard Model extensions. In this paper we discuss the reconstruction of the radiative penguin decays ${mathrm{B^0}} ightarrow {mathrm{K}^{*0}}gamma$, ${mathrm{B^0_{mathrm{s}}}} ightarrow phi gamma$, ${mathrm{B^0}} ightarrow omega gamma$, the electroweak penguin decay ${mathrm{B^0}} ightarrow {mathrm{K}^{*0}}mu^+mu^-$, the gluonic penguin decays ${mathrm{B^0}} ightarrow {mathrm{K^0_S}}phi$, ${mathrm{B^0_{mathrm{s}}}} ightarrow phi phi$ and the decay ${mathrm{B^0_{mathrm{s}}}} ightarrow mu^+ mu^-$ at LHCb. The selection criteria, evaluated efficiencies, expected annual yields and $mathcal{B}/mathcal{S}$ estimates are presented.