  I present the results of Monte-Carlo orbital simulations of Galactic Neutron
Stars (NSs). The simulations take into account the up-to-date observed NS space
and velocity distributions at birth, and account for their formation rate. I
simulate two populations of NSs. Objects in the first population were born in
the Galactic disk at a constant rate, in the past 12 Gyr. Those in the second
population were formed simultaneously 12 Gyr ago in the Galactic bulge. I
assume that the NSs born in the Galactic disk comprise 40% of the total NS
population. Since the initial velocity distribution of NSs is not well known, I
run two sets of simulations, each containing 3x10^6 simulated NSs. One set
utilizes a bimodal initial velocity distribution and the other a unimodal
initial velocity distribution, both are advocated based on pulsars
observations. In light of recent observational results, I discuss the effect of
dynamical heating by Galactic structure on NS space and velocity distributions
and show it can be neglected. I present catalogue of simulated NS space and
velocity vectors in the current epoch, and catalogue of positions, distances
and proper motions of simulated NSs, relative to the Sun. Assuming there are
10^9 NSs in the Galaxy, I find that in the solar neighborhood the density of
NSs is about 2-4x10^-4 pc^-3 and their scale height is about 0.3-0.6 kpc
(depending on the adopted initial velocity distribution). These catalogue can
be used to test the hypothesis that some radio transients are related to these
objects.
