Based on a new version of the Hipparcos catalog and currently available radial velocity data, we have searched for stars that either have encountered or will encounter the solar neighborhood within less than 3 pc in the time interval from -2 Myr to +2 Myr. Nine new candidates within 30 pc of the Sun have been found. To construct the stellar orbits relative to the solar orbit, we have used the epicyclic approximation. We show that, given the errors in the observational data, the probability that the well-known star HIP 89 825 (GL 710) encountering with the Sun most closely falls into the Oort cloud is 0.86 in the time interval 1.45 ± 0.06 Myr. This star also has a nonzero probability, 1 × 10-4, of falling into the region d < 1000 AU, where its influence on Kuiper Belt objects becomes possible.