  We study here the gravitational collapse of a matter cloud with a
non-vanishing tangential pressure in the presence of a non-zero cosmological
term. Conditions for bounce and singularity formation are derived for the
model. It is also shown that when the tangential pressures vanish, the bounce
and singularity conditions reduce to that of the dust case studied earlier. The
collapsing interior is matched with an exterior which is asymptotically de
Sitter or anti de Sitter, depending on the sign of cosmological constant. The
junction conditions for matching the cloud to exterior are specified. The
effect of the cosmological term on apparent horizons is studied in some detail,
and the nature of central singularity is analyzed. We also discuss here the
visibility of the singularity and implications for the cosmic censorship
conjecture.

General Relativity and Quantum Cosmology;High Energy Physics - Theory