05 - LHCbRare 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 mathrmB0rightarrowmathrmK∗0gamma, mathrmBmathrms0rightarrowphigamma, mathrmB0rightarrowomegagamma, the electroweak penguin decay mathrmB0rightarrowmathrmK∗0mu+mu−, the gluonic penguin decays mathrmB0rightarrowmathrmKS0phi, mathrmBmathrms0rightarrowphiphi and the decay mathrmBmathrms0rightarrowmu+mu− at LHCb. The selection criteria, evaluated efficiencies, expected annual yields and mathcalB/mathcalS estimates are presented