We have computed trajectories, distances and times of closest approaches to the Sun by stars in the solar neighbourhood with known position, radial velocity and proper motions. For this purpose, we have used a full potential model of the Galaxy that reproduces the local z-force, the Oort constants, the local escape velocity and the rotation curve of the Galaxy. From our sample, we constructed initial conditions, within observational uncertainties, with a Monte Carlo scheme for the 12 most suspicious candidates because of their small tangential motion. We find that the star Gliese 710 will have the closest approach to the Sun, with a distance of approximately 0.34 pc in 1.36 Myr in the future. We show that the effect of a flyby with the characteristics of Gliese 710 on a 100 au test particle disc representing the Solar system is negligible. However, since there is a lack of 6D data for a large percentage of stars in the solar neighbourhood, closer approaches may exist. We calculate parameters of passing stars that would cause notable effects on the solar disc. Regarding the birth cloud of the Sun, we performed experiments to reproduce roughly the observed orbital parameters such as eccentricities and inclinations of the Kuiper belt. It is now known that in Galactic environments, such as stellar formation regions, the stellar densities of new born stars are high enough to produce close encounters within 200 au. Moreover, in these Galactic environments, the velocity dispersion is relatively low, typically σ˜ 1-3 km s-1. We find that with a velocity dispersion of ˜1 km s-1 and an approach distance of about 150 au, typical of these regions, we obtain approximately the eccentricities and inclinations seen in the current Solar system. Simple analytical calculations of stellar encounters effects on the Oort Cloud are presented.