The results of first-principles crystal structure optimization for the bulk rutile-type tin dioxide and its (110) and (001) surfaces as obtained by applying the siesta code, that incorporates norm-conserving pseudopotentials and strictly localized basis of pseudoatomic orbitals, are summarized. The relaxation near the (110) surface has been studied with the use of small supercells Sn 6 O 10 and Sn 6 O 12 , representing reduced and stoichiometric compositions, respectively, and compared with previously known results of other simulations. Further on, the effect of relaxation has been studied for a larger (stoichiometric) supercell Sn 10 O 20 . While qualitatively the same as obtained for small supercells, the relaxation pattern shows however numerical differences. The relaxation study at the (001) surface shows, as the major effect, the inward relaxation of the upper tin layer and the outward displacement of upper oxygen atoms (by ≈0.3Å) with respect to it. When going deep into the crystal, the values of Sn-Sn interplane distances and O-Sn interplane displacements fluctuate around the corresponding values in the bulk and decrease. They are not yet stabilized near the 5th tin layer from the surface, implying the need to consider even larger supercells for the accurate numerical estimations of the relaxation at the surface.