  The Casimir forces on two parallel plates moving by uniform proper
acceleration in static de Sitter background due to conformally coupled massless
scalar field satisfying Dirichlet boundary conditions on the plates is
investigated. 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.
