  We investigate the thermal Casimir force between two parallel plates made of
different isotropic materials which are separated by a uniaxial anisotropic
film. Numerical computations of the Casimir pressure at T=300K are performed
using the complete Lifshitz formula adapted for an anisotropic intervening
layer and in the nonrelativistic limit. It is shown that the standard
(nonrelativistic) theory of the van der Waals force is not applicable in this
case, because the effects of retardation contribute significantly even for film
thicknesses of a few nanometers. We have also obtained simple analytic
expressions for the classical Casimir free energy and pressure for large film
thicknesses (high temperatures). Unlike the case of isotropic intervening
films, for two metallic plates the classical Casimir free energy and pressure
are shown to depend on the static dielectric permittivities of an anisotropic
film. One further interesting feature is that the classical limit is achieved
at much shorter separations between the plates than for a vacuum gap. Possible
applications of the obtained results are discussed.
