  The Casimir force for charge-neutral, perfect conductors of non-planar
geometric configurations have been investigated. The configurations are: (1)
the plate-hemisphere, (2) the hemisphere-hemisphere and (3) the spherical
shell. The resulting Casimir forces for these physical arrangements have been
found to be attractive. The repulsive Casimir force found by Boyer for a
spherical shell is a special case requiring stringent material property of the
sphere, as well as the specific boundary conditions for the wave modes inside
and outside of the sphere. The necessary criteria in detecting Boyer's
repulsive Casimir force for a sphere are discussed at the end of this thesis.
