HF-DFT LCAO hybrid simulations on (0 0 1) and (1 1 0) surfaces of orthorhombic and (0 0 1) surface of cubic SrHfO3 perovskite are performed using a single slab model framework. PBE0 exchange-correlation functional is used for this study. The energy and crystal structure of bulk cubic and orthorhombic phases are calculated and compared. It is found that orthorhombic modification is more stable than cubic one by 24 kJ mol–1 per formula unit.Calculated average surface energies and relaxation energies proved to be similar for all orthorhombic surfaces. Atomic displacements along the direction normal to the surface are primarily determined by the type of termination and weakly depend on the surface indices. Without symmetry constraining, cubic surfaces are unstable with respect to reconstruction to corresponding orthorhombic surfaces at T = 0 K.While the upright displacements of the topmost atoms are mainly due to additional distortions of the surface octahedra, the lateral atomic displacements are closely related to changing in surface group tilting. The approach for the analysis of surface octahedron tilting is proposed and applied to the relaxed orthorhombic surfaces of SrHfO3 perovskites. It is shown that the HfO5 group on the HfO2-termianted surfaces undergoes a considerable turn upon relaxation, resulting in alignment of Hf–O–Hf bonds to corresponding pseudo-cubic directions.