CePO4 monazite is an important radiation-resistant material that may act as a potential minor actinides waste form. Here, we present the results of the calculations for the basic radiation defect modellings in CePO4 crystals, along with the examination of their defect formation energies and effect of the defect concentrations. This study focused on building a fully-relaxed CePO4 model with the step iterative optimization from the DFT-GGA calculations using the VASP and CASTEP databases. The results show that the Frenkel defect configuration resulting from the center interstitials has a lower energy when compared to two adjacent orthophosphate centers (the saddle point position). High formation energies were found for all the types of intrinsic Frenkel and vacancy defects. The formation energies conform to the following trend (given in the decreasing order of energy): Ce Frenkel (12.41 eV) > O Frenkel (11.02 eV) > Ce vacancy (9.09 eV) > O vacancy (6.69 eV). We observed almost no effect from the defect concentrations on the defect formation energies.