The radiation resistance of the monazite LaPO4 and the compound YbPO4 (zircon structure type) has been investigated using the computer simulation. The number of Frenkel pairs, which are formed in the structure of these minerals after the passage of a primary knock-on thorium atom with an energy of 30 keV, has been calculated by the molecular dynamics method. The formation of Frenkel pairs and their recombination in the motion of recoil nuclei in the structure of the studied minerals have been discussed. It has been shown that the probability of the “survival” of Frenkel pairs in the LaPO4 monazite is significantly lower than in the YbPO4 compound. The tendency of these minerals toward amorphization under radiation damage has been described numerically. The obtained results have demonstrated that one of the main factors determining the radiation resistance of orthophosphates LnPO4 is the type of crystal structure, and the compounds with the monazite structure are more radiation resistant than the compounds with the zircon structure.