  We determine the effect of Lorentz invariance violation in the vacuum energy
and stress between two parallel plates separated by a distance $L$, in the
presence of a massive real scalar field. We parametrize the Lorentz-violation
in terms of a symmetric tensor $h^{\,\mu\nu}$ that represents a constant
background. Through the Green's function method, we obtain the global Casimir
energy, the Casimir force between the plates and the energy density in a closed
analytical form without resorting to perturbative methods. With regards to the
pressure, we find that $\mathcal{F}_c(L)=\mathcal{F}_0(\tilde{L})/\sqrt{-{\rm
det}\, h^{\,\mu\nu}}$, where $\mathcal{F}_0$ is the Lorentz-invariant
expression, and $\tilde{L}$ is the plate separation rescaled by the component
of $h^{\,\mu\nu}$ normal to the plates, $\tilde{L}=L/\sqrt{-h^{nn}}$. We also
analyze the Casimir stress including finite-temperature corrections. The local
behavior of the Casimir energy density is also discussed.
