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 3 \times 10 ^ { 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 - 4 \times 10 ^ { -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 .