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The numerical model of the shock-drift acceleration of interstellar pickup protons at the three-dimensional solar wind termination shock is presented. The model takes into account multiple reflections of the particles at and passing through the shock in the forward and reverse directions. The processes of the multiple interactions with the shock are possible due to pitch-angle scattering of protons in the upstream and downstream parts of the plasma flow. The model takes into account variations of the magnetic field direction in a vicinity of the shock connected with passing of the sector structure of the interplanetary magnetic field through the shock front at low ecliptic latitudes. The main advantage of the model is the self-consistent treatment of protons and interstellar hydrogen atoms, which are described kinetically and interact with protons through the resonant charge exchange process. The shock-drift acceleration can explain the fluxes of energetic protons measured at the Voyager~1/2 spacecraft after the termination shock crossings. No any pre-acceleration in the supersonic solar wind is needed to explain the data. The results of the model can be used to interpret the interstellar atom fluxes measured at the IBEX spacecraft.