This study assessed the response function of a p-type and n-type coaxial high-purity germanium (HPGe) detector via Monte Carlo simulations. MCNPX was employed to model the Coaxial Ge detectors, and for a precise simulation, the dimensions of the dead layer of germanium crystals were added. The dead layer was separated into front and lateral surfaces, and the thickness of each dead layer was modeled. In this work, the simulated detectors have been performed at different energy lines using a radioactive source Eu-152 to study the response function of each with dead layer variations for the front dead layer and study the range of relative deviation of the Monte Carlo simulation outputs from the manufactured declared data. The results proved that the n-type coaxial high-purity germanium (HPGe) detector is more sensitive to the dead layer change than p-type with a thick change by 0.02 mm. This research has significant effects on the efficiencies of the radiation detection systems in the energy range ~ (120-1410) KeV.