The change of resistance of SnO2 upon the change of oxygen partial pressure-a well known sensor effect-is studied theoretically. A linearised drift-diffusion model is used. The boundary conditions are formulated in terms of reaction rate equations. Resistance vs. time curves as well as the evolution of the concentration profiles of electrons and oxygen vacancies are numerically calculated anti discussed. Analytical approximations are derived for the corresponding time constants. Relevance of the model for commercial sensors is discussed.