  Symbiotic X-ray binaries (SyXBs) comprise a rare class of low-mass X-ray
binaries. We study the Galactic SyXBs, which we consider as detached binaries
composed of low-mass giants and wind-fed neutron star companions, by simulation
of the interaction of a magnetized neutron star (NS) with its environment and
utilizing a population synthesis code. We focus mainly on the parameters that
influence observational appearance of the SyXB: the donor wind velocity (vw)
and the angular momentum distribution in the shell of matter settling onto NS.
We estimate the birthrate of SyXB as $\sim 4.1\times 10^{-5}$ yr$^{-1}$ to $
\sim 6.6\times 10^{-6}$ yr$^{-1}$ and their number in the Galaxy as $\sim$(100
-- 1000). Assumed stellar wind velocity from cool giants is the input parameter
that influences the model SyXBs population most.
  Among known SyXBs or candidate systems, 4U 1954+31 and IGR J16358-4724 in
which NS have very long spin periods may host quasi-spherically accreting NSs.
GX 1+4 has a peculiar long-term spin behaviour and it may also be a
quasi-spherical wind-accreting source. We cannot identify whether there are
wind-fed accretion disks in 4U 1700+24, Sct X-1, IRXS J180431.1-273932 and 2XMM
J174016.0-290337.
