It is generally believed that our Sun will expand enormously twice during the late stages of its life. A first expansion will happen when it reaches the red giant branch (RGB). A second expansion will occur on the asymptotic giant branch (AGB), and the Sun's radius will attain its maximum values during the stage of thermal pulses on the asymptotic giant branch. We have examined the ultimate fate of the terrestrial planets considering various existing models of the Sun's future evolution. The basic factors, which are essential in our analysis, are the solar mass loss and the drag forces acting on the planets. Both factors are only known with large uncertainties, thus, we cannot claim that our results are definitive. But the conclusion we draw from our study is that Mercury will evaporate during the RGB, and Venus will most probably be destroyed as well. The Earth's fate still remains controversial, but according to the existing evolution sequences for solar models, it is likely that our planet will evaporate during the giant stage of the Sun. Mars will most probably survive. Our investigation shows that tidal interaction should play a significant role in reducing separation between Venus and the Sun, and to a smaller extent, between Earth and the Sun. Moreover, in this study we considered the spiralling-in of planets as they are engulfed by the Sun. Our results indicate that the Earth might actually avoid evaporation when being engulfed by the Sun, provided this happens only during brief periods of thermal pulses at the terminal AGB stage.