In a previous paper we have illustrated the concept of resonant flow instability of the trapped modes both in a 1-D slab model and a 1-D cylindrical model for a coronal plume in a cold plasma. We found that much larger values of the velocity shear are needed for Kelvin-Helmholtz than for resonant instability to occur. The aim of this paper is to study the effect of a non-zero plasma pressure on the eigenmodes of the plume structure. We show that the instability most probably to occur in coronal plumes is due to the resonant coupling of slow body modes to local resonant Alfve´n waves. These instabilities could lead to disruption of the coronal plumes and to the mixing with interplume plasma. ©2000 American Institute of Physics.