Investigation of loop penguin decays of beauty hadrons seems promising in testing the predictions of the Standard Model of electroweak and strong interactions and in seeking new phenomena beyond the Standard Model. The possibility of studying the radiative penguin decays B^0 -> K*^0 gamma, B^0_s -> phi gamma and B^0 -> omega gamma and the gluonic penguin decays B^0 -> phi K*^0_s and B^0_s -> phi phi in LHCb experiments is discussed.