  In this paper we consider a Lorentz-breaking extension of the theory for a
real massive scalar quantum field in the region between two large parallel
plates, with our manner to break the Lorentz symmetry is CPT-even, aether-like.
For this system we calculated the Casimir energy considering different boundary
conditions. It turns out to be that the Casimir energy strongly depends on the
direction of the constant vector implementing the Lorentz symmetry breaking, as
well as on the boundary conditions.
