Motivated by the potential high temperature superconductivity in hydrogen-rich materials, high-pressure structures of ErH3 and HoH3 were studied by using genetic algorithm method. Our calculations indicate that both ErH3 and HoH3 transform from P-3c1 structure to a monoclinic C2/m structure at about 15 GPa, and then transforms into a cubic Fm-3m structure at about 40 GPa. ErH3 and HoH3 adopt the same P6₃/mmc structure with space group P6₃/mmc at above about 220 and 196 GPa, respectively. For ErH3, the P6₃/mmc phase is stable up to at least 300 GPa, while for HoH3, a phase transformation P6₃/mmc → Cmcm occurs at about 216 GPa, and the Cmcm phase is stable up to at least 300 GPa. The P-3c1 ErH3 and HoH3 are calculated to demonstrate non-metallic character, and the other phases are all metallic phases.