Gamma-ray shielding properties of ilmenite-magnetite (I-M) concrete and polyboron are measured with an NaI(Tl) detector. The detector response function is studied, and the inverted detector response matrix is generated. Using this inverted response matrix, the pulse-height spectra of gamma rays transmitted through the shields are converted into photon spectra, and the respective dose rates are calculated. The instantaneous relaxation lengths and the buildup factors for gamma rays from a 252Cf source penetrating I-M concrete and polyboron slabs are reported. Buildup factors and instantaneous relaxation lengths are fitted to the appropriate functions, and the related coefficients are also reported.