Resonance self-shielding occurs as the result of flux depressions at resonance peaks. The group self-shielding factor is defined as the ratio of the effective flux-weighted cross section to the average cross section. Given a constant background cross section, σ, as well as a temperature and an energy group, the shielding factor of an element can be approximated by simple formulas employing two- or three-group effective parameters. These are λ, η, and p—an effective base (potential scattering) cross section, an effective peak cross section, and an effective ratio of the base cross section to the average of the resonance total cross section, respectively. The use of resonance group parameters eliminates the problem of σ- interpolation. Furthermore, through a certain interpretation of these parameters, the σ- ambiguity is also cleared up. The constant background, σ, required to represent the actual interaction of the shielded resonance series with background resonance series, is a linear expression in the number densities and the λ’s of the background elements. The  σ- iteration technique, currently in use, is shown to be rather inaccurate.