  In this paper we consider a Lorentz-breaking scalar field theory within the
Horava-Lifshtz approach. We investigate the changes that a space-time
anisotropy produces in the Casimir effect. A massless real quantum scalar field
is considered in two distinct situations: between two parallel plates and
inside a rectangular two-dimensional box. In both cases we have adopted
specific boundary conditions on the field at the boundary. As we shall see, the
energy and the Casimir force strongly depends on the parameter associated with
the breaking of Lorentz symmetry and also on the boundary conditions.
