  Extreme accretion in X-ray pulsars (XRPs) results in radiation-driven
outflows launched from the inner parts of the accretion disc. The outflows
affect the apparent luminosity of the XRPs and their pulsations through the
geometrical beaming. We model processes of geometrical beaming and pulse
formation using Monte Carlo simulations. We confirm our earlier statement that
strong amplification of luminosity due to the collimation of X-ray photons is
inconsistent with a large pulsed fraction. Accounting for relativistic
aberration due to possibly high outflow velocity ($\sim 0.2c$) does not affect
this conclusion. We demonstrate that the beaming causes phase lags of
pulsations. Within the opening angle of the accretion cavity formed by the
outflows, phase lags tend to be sensitive to observers viewing angles.
Variations in outflow geometry and corresponding changes of the phase lags
might influence the detectability of pulsation in bright X-ray pulsars and
ULXs. We speculate that the strong geometrical beaming is associated with large
radiation pressure on the walls of accretion cavity due to multiple photons
reflections. We expect that the mass loss rate limits geometrical beaming:
strong beaming becomes possible only under sufficiently large fractional mass
loss rate from the disc.
