  We study the effects on the number counts of sub-millimetre galaxies due to
gravitational lensing. We explore the effects on the magnification cross
section due to halo density profiles, ellipticity and cosmological parameter
(the power-spectrum normalisation $\sigma_8$). We show that the ellipticity
does not strongly affect the magnification cross section in gravitational
lensing while the halo radial profiles do. Since the baryonic cooling effect is
stronger in galaxies than clusters, galactic haloes are more concentrated. In
light of this, a new scenario of two halo population model is explored where
galaxies are modeled as a singular isothermal sphere profile and clusters as a
Navarro, Frenk and White (NFW) profile. We find the transition mass between the
two has modest effects on the lensing probability. The cosmological parameter
$\sigma_8$ alters the abundance of haloes and therefore affects our results.
Compared with other methods, our model is simpler and more realistic. The
conclusions of previous works is confirm that gravitational lensing is a
natural explanation for the number count excess at the bright end.
