The work which has been done on cement-polymer composite based shielding materials was comprehensively described in the present article, the choice of the study presented here is based on the choice of the researches. The new Hyperbranched Poly Amino-Ester-block-Poly Caprolactone-Polyurathane Plaster-concrete composites mixed with different percentage soft lead oxide and arsenic oxide is used to research gamma-ray shielding and thermal conductivity characteristics. The synthesis of new Hyperbranched Poly Amino-Ester-block-Poly Caprolactone-Polyurathane copolymer was achieved by Atom Transfer Reaction and Condensation Polymerization methods. The characterization of Hyperbranched Poly Amino-Ester-block-Poly Caprolactone-Polyurathane Plaster was made with the Nuclear Magnetic Resonance, Fourier Transform Infrared Spectroscopy, Differential Scanning Calorimetry, Gel Permeation Chromatography, Thermogravimetric Analysis, Scanning Electron Microscope methods. The transmitted fluxes of gamma-rays that were emitted from Eu152 source was detected by a High Purity Germanium (HPGe) detector system at Karadeniz Technical University-Department of Physics in Trabzon and analyzed by a GammaVision (Version:6.07-Ortec, Oak Ridge, TN) computer program. The composite phase change materials including 89, 87, 69, 67% Portland cement, 1% and 3% PU-Plaster, 10% and 30% weight percent lead oxide and arsenic oxide was irradiated in the various gamma ray photon energy region (121.78, 344.28, 778.90, 964.08, 1085.87, 1112.07, and 1408.01 keV) for 3600 seconds. Then, linear attenuation coefficients, mass attenuation coefficients, half-value layer, tenth value layer, mean free path, radiation protection efficiency, and gamma-rays absorption of concrete-the Hyperbranched Poly Amino-Ester-block-Poly Caprolactone-Polyurathane copolymers specimens were experimentally investigated. Thermal properties and morphological analysis of the irradiated substances were explored handling differential scanning calorimetry, thermogravimetric analysis, and scanning electron microscope methods of the nano lead oxide and arsenic oxide including composite phase change material via gamma irradiation were submitted. Moreover, the effect of the Hyperbranched Poly Amino-Ester-block-Poly Caprolactone-Polyurathane amount on the radiation attenuation of the composite material was investigated. Gamma attenuation experiments have been performed to specify lead equivalent values for the improved composite material. The composite equivalent thickness values from 0.5 to 0.6 cm sample thickness and 0.665 cm radius were obtained. Via crosschecking the acquired data from concrete samples with and without lead and arsenic, it was observed that, if the powder of lead oxide and arsenic oxide to cement ratio of 10% and 30% by weight is added in the concrete mixture, the concrete-the Hyperbranched Poly Amino-Ester-block-Poly Caprolactone-Polyurathane composite can be used as a suitable shield against gamma rays. Also, mass attenuation coefficients were calculated as theoretical with the National Institute of Standards and Technology(NIST)-XCOM database. The thermal conductivity coefficient and the heat capacity of the composites were determined.