In this work, new composites in the form of paste of high density polyethylene (HDPE), commercial borax (BX), sand and Portland cement were designed with different concentrations of each, constructed and tested for Am-241-Be neutrons and Co-60 gamma rays. The design depended on the calculated values of the effective removal cross section (Sigma(R)), total macroscopic scattering cross section (Sigma(t)), slowing down power (SDP), and moderating ratio (mr) for neutrons and volumetric density and the total mass attenuation coefficients (MAC = mu/rho)for gamma radiation. The results indicated that a composite of 12.5% HDPY, 37.5% BX, 25%cement and 25% sand has the highest attenuation parameter for both Am-241-Be neutrons and Co-60 gamma radiation. This radiation shielding paste has the advantages over all available shields of being; low cost, light and durable to be formed, non-toxic and has higher radiation attenuation parameters as compared with all available shields.