By means of the B3LYP and B3PW hybrid exchange-correlation functionals, as it is included in the CRYSTAL computer code, we performed ab initio computations for BaSnO3 and BaZrO3 perovskite (001) surfaces. For BaSnO3 and BaZrO3 perovskite (001) surfaces, with a few exceptions, all atoms of the upper surface layer relax inwards, all atoms of the second surface layer relax outwards, and all third layer atoms, again, relax inwards. The relaxation of BaSnO3 and BaZrO3 (001) surface metal atoms for upper two surface layers, for both BaO and BO2-terminations, as a rule, are considerably larger than the relaxation of relevant oxygen atoms. The BaO (1.30 eV) and ZrO2-terminated (1.31 eV) BaZrO3 (001) surface energies are almost equal. The BaZrO3 perovskite BaO (4.82 eV) and ZrO2-terminated (4.48 eV) (001) surface Г-Г band gaps are reduced regarding the respective bulk Г-Г band gap value (4.93 eV). The B–O chemical bond populations in BaSnO3 and BaZrO3 perovskite bulk always are smaller than near their SnO2 and ZrO2-terminated (001) surfaces, respectively.