A pseudopotential plane-wave based density functional theory simulations of the hydrogen adsorption on rutile SnO2 (110) surface is reported. It is found that on doping with trivalent indium, the surface becomes unstable due to the formation of bridging oxygen vacancies. At sufficiently low doping level, the surface stabilizes at an oxygen vacancy to indium ratio of 1:2. Our calculations predict that at a higher doping level of 9 at.% this ratio becomes larger, and point out a way to synthesize p -type conducting SnO2 thin films. The binding energy of SnO2 (110) surface with adsorbed hydrogen atoms display a maximum at 3-6 at. % of indium doping. This is in good agreement with the experimental results obtained from the SnO2-based hydrogen sensor's sensitivity measurements given by Drake [J. Appl. Phys. 101, 104307 (2007)]. The theoretical modeling explains that the calcinations treatment can critically affect the sensitivity of the hydrogen sensor due to the enhancement of the binding energy between the SnO2 surface and the adsorbed hydrogen atoms.