  We study the effects of the minimal extension of the standard model including
Lorentz violation on the Casimir force between two parallel conducting plates
in vacuum. We provide explicit solutions for the electromagnetic field using
scalar field analogy, for both the cases in which the Lorentz violating terms
come from the CPT-even or CPT-odd terms. We also calculate the effects of the
Lorentz violating terms for a fermion field between two parallel conducting
plates and analyze the modifications of the Casimir force due to the
modifications of the Dirac equation. In all cases under consideration, the
standard formulas for the Casimir force are modified by either multiplicative
or additive correction factors, the latter case exhibiting different dependence
on the distance between the plates.
