  In this paper we classify static plane symmetric spacetimes according to
their matter collineations. These have been studied for both cases when the
energy-momentum tensor is non-degenerate and also when it is degenerate. It
turns out that the non-degenerate case yields either {\it four}, {\it five},
{\it six}, {\it seven} or {\it ten} independent matter collineations in which
{\it four} are isometries and the rest are proper. There exists three
interesting cases where the energy-momentum tensor is degenerate but the group
of matter collineations is finite-dimensional. The matter collineations in
these cases are either {\it four}, {\it six} or {\it ten
