A previously unknown thermodynamically stable high-pressure phase of BeF₂ has been predicted using the evolutionary algorithm USPEX. This phase occurs in the pressure range 18–27 GPa. Its structure has C2/c space group symmetry and contains 18 atoms in the primitive unit cell. Given the analogy between BeF₂ and SiO₂, silica phases have been investigated as well, but the new phase has not been observed to be thermodynamically stable for this system. However, it is found to be metastable and to have comparable energy to the known metastable phases of SiO₂, suggesting a possibility of its synthesis.