  The Casimir stress on a spherical shell in de Sitter background for massless
scalar field satisfying Dirichlet boundary conditions on the shell is
calculated. The metric is written in conformally flat form. Although the metric
is time dependent no particles are created. The Casimir stress is calculated
for inside and outside of the shell with different backgrounds corresponding to
different cosmological constants. The detail dynamics of the bubble depends on
different parameter of the model. Specifically, bubbles with true vacuum inside
expand if the difference in the vacuum energies is small, otherwise they
collapse.
