It is shown that in the solution of electromagnetic problems the compressibility of a medium can be characterized by a ``compressivity tensor,'' just as a permittivity tensor is used to characterize anisotropy. The effects of a compressible medium can be accounted for by a ``pressure displacement current,'' which depends on the spatial variation in pressure, and by an equivalent volume density of charge, which is proportional to the pressure deviation from the mean. The constitutive parameter tensors are given in both dyadic and matrix forms. With the suggested representations, the solution of electromagnetic problems in an anisotropic and compressible plasma can proceed on a systematic basis. It is also shown that with a constant, externally applied magnetic field, the electromagnetic fields can be decomposed into longitudinal and transverse components. A complete formal solution is given for the case where there is no longitudinal variation.