  We investigate the distortions due to this shear in the microlensing light
curves and in the astrometric microlensing centroid shift trajectories. As
expected, the light curve deviation increases as the shear increases and the
impact parameter decreases. Although the light curve in the presence of a small
shear is similar to the simple Paczynski curve with a slightly smaller impact
parameter, the detailed difference between the light curve with and without
shear reflects the direction and the magnitude of the shear. The centroid shift
trajectory also deviates from a simple ellipse in the presence of shear. The
distortion of the centroid shift trajectory increases as the impact parameter
decreases, and the shape of the trajectory becomes complicated when the impact
parameter becomes small enough. The magnitude of the maximum distortion depends
on the magnitude and the direction of the shear. For a source trajectory in a
given direction, the time of the maximum distortion depends mostly on the
impact parameter and hardly on the shear. It is possible to determine the
magnitude of the shear and its direction if both the time and the magnitude of
the maximum astrometric distortion are measured. The magnitude of the shear
produced by the Galactic bulge or a globular cluster falls in the range
10^{-6}--10^{-4} in normalized units. Although the actual determination of the
shear from the Galactic sub-structures will not be easy due to complications
such as binary companion, future large scale microlensing experiments may
enable us to determine the shear in some high amplification events, leading
eventually to mapping the Galactic mass distribution.
