  We adopt the Dirac model for graphene and calculate the Casimir interaction
energy between a plane suspended graphene sample and a parallel plane ideal
conductor. We employ both the Quantum Field Theory (QFT) approach, and the
Lifshitz formula generalizations. The first approach turns out to be the
leading order in the coupling constant of the second one. The Casimir
interaction for this system appears to be rather weak but experimentally
measurable. It exhibits a strong dependence on the mass of the quasi-particles
in graphene.
