  The ``Eshelby problem" refers to the response of a 2-dimensional elastic
sheet to cutting away a circle, deforming it into an ellipse, and pushing it
back. The resulting response is dominated by the so-called ``Eshelby Kernel"
which was derived for purely elastic (infinite) material, but has been employed
extensively to model the redistribution of stress after plastic events in
amorphous solids with finite boundaries. Here we discuss and solve the Eshelby
problem directly for amorphous solids, taking into account possible screening
effects and realistic boundary conditions. We find major modifications compared
to the classical Eshelby solution. These modification are needed for modeling
correctly the spatial responses to plastic events in amorphous solids.
