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 {B⁰_d}\rightarrow {K^*0}\gamma , {B⁰ _s}\rightarrow \phi \gamma , {B⁰_d}\rightarrow \omega \gamma , {\Lambda_b}\rightarrow {\Lambda }\gamma , the electroweak penguin decays {B⁰_d}\rightarrow K^*0\mu ⁺\mu ^-, {B⁺_u}\rightarrow {K⁺}\mu ⁺\mu ^-, the gluonic penguin decays {B⁰_d} \rightarrow \phi {K⁰_S}, {B⁰_s} \rightarrow \phi \phi and the decay {B⁰ _s} \rightarrow \mu ⁺ \mu ^- at LHCb. The selection criteria, evaluated efficiencies, expected annual yields and B/S estimates are presented.

PACS numbers: 14.40.Nd, 12.60.--i