Refractory high entropy alloys constituted of refractory alloying elements, such as W, Zr, Nb, Ti, Mo, Ta, and Hf, are of great interest due to their widespread use in areas such as the defense, aerospace, and nuclear power generation industries. Refractory high entropy alloys are one of the subgroups of high entropy alloys and are evaluated as great candidates for replacements of superalloys commonly used at high temperatures due to their good mechanical properties and corrosion and oxidation resistance at high temperatures. The motivation for performing this study is that there is currently no comprehensive analysis of the radiation shielding abilities of this new type of high entropy alloys. The purpose of the study was to evaluate the radiation attenuation parameters such as mass and linear attenuation coefficients, half value layer, mean free path, effective atomic number, and buildup factors of the refractory high entropy alloys, Al0.5Mo0.5NbTa0.5TiZr, Al0.25NbTaTiZr, HfMoScTaZr, Nb40Ti25Al15V10Ta5Hf3W2, NbCrMo0.5Ta0.5TiZr, Ti2VNbMoZr, and W23Mo23V17Cr8Ta7Fe22 by using EpiXS software. The mass attenuation coefficients of the alloys were also calculated by XCOM, a well-known code, to see the consistency of the obtained values. It was concluded that HfMoScTaZr and W23Mo23V17Cr8Ta7Fe22 have more shielding features, while Ti2VNbMoZr has the lowest shielding ability among the alloys.