An approach to the problem of the Casimir force on magnetodielectric bodies is outlined, which is based on the calculation of the ground-state Lorentz force acting on the polarization and magnetization charges and currents that constitute the bodies within the framework of linear, macroscopic electrodynamics. As an application, planar structures are considered and a correct generalization of Casimir's original formula to the case where the two highly reflecting plates are embedded in a medium is given.