  We analyze the Casimir densities and forces associated with a massive scalar
quantum field confined between two parallel plates in a D-dimensional cosmic
string spacetime. The plates are placed orthogonal to the string and the field
obeys the Robin boundary conditions on them. The boundary-induced contributions
are explicitly extracted in the vacuum expectation values (VEVs) of the field
squared and energy-momentum tensor for both single and two plates. The VEV of
the energy-momentum tensor, in additional to the diagonal components, contains
an off-diagonal component corresponding to the shear stress. The latter
vanishes on the plates in special cases of Dirichlet and Neumann boundary
conditions. For points outside the string core the topological contributions in
the VEVs are finite on the plates. Near the string the VEVs are dominated by
the boundary-free part, whereas at large distances the boundary-induced
contributions dominate. Due to the nonzero off-diagonal component of the vacuum
energy-momentum tensor, in addition to the normal component, the Casimir forces
have nonzero component parallel to the boundary. Unlike the problem on the
Minkowski bulk, the normal forces acting on the separate plates, in general, do
not coincide. Another difference is that in the presence of the cosmic string
the Casimir forces for Dirichlet and Neumann boundary conditions differ. For
Dirichlet case the normal Casimir force does not depend on the curvature
coupling parameter. This is not the case for other boundary conditions. A new
qualitative feature induced by the cosmic string is the appearance of the shear
stress acting on the plates. The corresponding force is directed along the
radial coordinate and vanishes for Dirichlet and Neumann cases. Depending on
the parameters of the problem, the radial component of the shear force can be
either positive or negative.
