Electromagnetic Casimir stresses are of relevance to many technologies based on mesoscopic devices such as microelectromechanical systems embedded in dielectric media, Casimir induced friction in nanomachinery, microfluidics, and molecular electronics. Computation of such stresses based on cavity QED generally requires numerical analysis based on a regularization process. The scheme described below has the potential for wide applicability to systems involving realistic inhomogeneous media. From a knowledge of the spectrum of the stationary modes of the electromagnetic field the scheme is illustrated by estimating numerically the Casimir stress on opposite faces of a pair of perfectly conducting planes separated by a vacuum and the change in this result when the region between the plates is filled with an incompressible inhomogeneous nondispersive dielectric.