Gamma ray shielding effectiveness of superconductors with a high mass density has been investigated. We calculated the mass attenuation coefficients, the mean free path (mfp) and the exposure buildup factor (EBF). The gamma ray EBF was computed using the Geometric Progression (G-P) fitting method at energies 0.015-15 MeV, and for penetration depths up to 40 mfp. The fast-neutron shielding effectiveness has been characterized by the effective neutron removal cross-section of the superconductors. It is shown that CaPtSi3, CaIrSi3, and Bi2Sr2Ca1Cu2O8.2 are superior shielding materials for gamma rays and Tl0.6Rb0.4Fe1.67Se2 for fast neutrons. The present work should be useful in various applications of superconductors in fusion engineering and design. (C) 2014 Elsevier Ltd. All rights reserved.