YPO₄, ScPO₄, and LuPO₄ crystallize in the tetragonal system conforming to space group model I4₁/ amd (D¹⁹_4h, No. 141), Z = 4. The refined crystal structures have been determined from three-dimensional single-crystal X-ray diffraction data. Final least-squares full-matrix refinement yielded respective R-values of 0.024, 0.028, and 0.038. The metal atom in each compound is 8-coordinated to oxygen atoms. The resultant polyhedron is viewed as two interpenetrating tetrahedra forming a bis-bisphenoid (D_2d). The phosphate group in each compound is a distorted tetrahedron. Important bond and contact distances and bond angles as well as Ortep-II drawings are presented to foster a wider base for future investigations related to potential employment of lanthanide orthophosphates as hosts for radioactive nuclear waste.