The known nearby stars, moving in front of the background of distant s
tars and galaxies, create ''weak gravitational lensing'' variations in
their positions. These variations may be measurable with the HST, and
they may allow a direct mass determination for the nearby stars. The
cross-section for the HST measurable astrometric effect is much larger
than the cross-section for the photometric effect which is measurable
from the ground. The mass determination will be easier for the fainte
r nearby lenses which will be discovered in future searches of faint h
igh proper motion stars.