The aim of this paper is to demonstrate the accuracy of our knowledge of close stellar passage distances in the pre-GAIA era .
We used the most precise astrometric and kinematic data available at the moment and prepared a list of 40 stars nominally passing ( in the past or future ) closer than 2 pc from the Sun .
We used a full gravitational potential of the Galaxy to calculate the motion of the Sun and a star from their current positions to the proximity epoch .
For this calculations we used a numerical integration in rectangular , Galactocentric coordinates .
We showed that in many cases the numerical integration of the star motion gives significantly different results than popular rectilinear approximation .
We found several new stellar candidates for close visitors in past or in future .

We used a covariance matrices of the astrometric data for each star to estimate the accuracy of the obtained proximity distance and epoch .
To this aim we used a Monte Carlo method , replaced each star with 10 000 of its clones and studied the distribution of their individual close passages near the Sun .
We showed that for contemporary close neighbours the precision is quite good but for more distant stars it strongly depends on the quality of astrometric and kinematic data .
Several examples are discussed in detail , among them the case of HIP 14473 .
For this star we obtained the nominal proximity distance as small as 0.22 pc 3.78 Myr ago .
However there exist strong need for more precise astrometry of this star since the proximity point uncertainty is unacceptably large .