  In this paper we study the Casimir effect for conformally coupled massless
scalar fields on background of Static dS$_{4+1}$ spacetime. We will consider
the general plane--symmetric solutions of the gravitational field equations and
boundary conditions of the Dirichlet type on the branes. Then we calculate the
vacuum energy-momentum tensor in a configuration in which the boundary branes
are moving by uniform proper acceleration in static de Sitter background.
Static de Sitter space is conformally related to the Rindler space, as a result
we can obtain vacuum expectation values of energy-momentum tensor for
conformally invariant field in static de Sitter space from the corresponding
Rindler counterpart by the conformal transformation.
