  We discuss the formalism of Balian and Duplantier for the calculation of the
Casimir energy for an arbitrary smooth compact surface, and use it to give some
examples: a finite cylinder with hemispherical caps, the torus, ellipsoid of
revolution, a "cube" with rounded corners and edges, and a "drum" made of disks
and part of a torus. We propose a model function which approximately captures
the shape dependence of the Casimir energy.
