BLIZARD calculating attenuation of -y-rays and neutrons may apply to cosmic ray shower theory and vice versa.The scope of the present treatment will include descriptions of the im portant radiation sources and of the individual attenuation processes. Fol lowing these are the calculations of attenuation in simple homogeneous shields as well as other problems in shield design, such as penetration after slant incidence, scattering, and the effects of voids in shields. Following this come some special methods for translating shield experiments into designs. Lastly, experiments and actual shield designs will be described briefly.