The Casimir stress on a cylindrical shell in the de Sitter background for a massless scalar field satisfying Dirichlet boundary conditions on the cylinder is calculated. The metric is written in conformally flat form to make maximal use of the Minkowski space calculations. In the framework of a toy model, we have considered the quantum vacuum effect in the evolution of a domain wall between a cylindrical or in fact circle region around the z axis in which vacuum isin and the remaining part of space where vacuum
