  We study the linear evolution of small perturbations in self-gravitating
fluid systems in two spatial dimensions; we consider both cylindrical and
cartesian (i.e., slab) geometries. The treatment is general, but the
application is to molecular clouds. We consider a class of equations of state
which heuristically take into account the presence of turbulence; in
particular, we consider equations of state which are {\it softer} than
isothermal. We take the unperturbed cloud configuration to be in hydrostatic
equilibrium. We find a class of wave solutions which propagate along a pressure
supported cylinder (or slab) and have finite (trapped) spatial distributions in
the direction perpendicular to the direction of propagation. Our results
indicate that the dispersion relations for these two dimensional waves have
similar forms for the two geometries considered here. Both cases possess a
regime of instability and a fastest growing mode. We also find the
(perpendicular) form of the perturbations for a wide range of wavelengths.
Finally, we discuss the implications of our results for star formation and
molecular clouds. The mass scales set by instabilities in both molecular cloud
filaments and sheets are generally much larger than the masses of stars.
However, these instabilities can determine the length scales for the initial
conditions for protostellar collapse.
