Six different composites of epoxy resin and Carbopol 974p polymer were prepared based on Carbopol 974p polymer concentrations of 0%, 5%, 10%, 15%, 20%, and 25%. The linear and mass attenuation coefficients, Half Value Layer (HVL), and mean free path (MFP) of these composites were determined using single-beam photon transmission in the energy range between 16.65 keV and 25.21 keV. This was carried out by determining the attenuation of ka1X-ray fluorescent (XRF) photons from niobium, molybdenum, palladium, silver, and tin targets. The results were compared with theoretical values of three types of breast material (Breast 1, Breast 2, Breast 3) and Perspex, which was calculated using a XCOM computer program. The results show that there were no significant differences in the attenuation coefficient values after the consequent Carbopol additions. Moreover, it was found that the mass attenuation coefficients of all tested composites were close to those of Perspex and the values for Breast 3. The HVL and MFP results showed that the E25 sample is closer to the results of the Perspex material with differences of (0.53–1.15%) and (0.51–1.20%), respectively. In addition, the densities of the fabricated samples were in the range of 1.102–1.170 g/cm3, which is in the range of human breast density. A computed tomography (CT) scanner was used to investigate the CT number values for the fabricated samples. The CT numbers of all samples were in the range of human breast tissue (24.53–40.28 HU). Based on these findings, the fabricated epoxy–Carbopol polymer is a good candidate for use as a breast phantom material.