  The zeta function regularization technique is used to study the Casimir
effect for a scalar field of mass $m$ satisfying Dirichlet boundary conditions
on a spherical surface of radius $a$. In the case of large scalar mass,
$ma\gg1$, simple analytic expressions are obtained for the zeta function and
Casimir energy of the scalar field when it is confined inside the spherical
surface, and when it is confined outside the spherical surface. In both cases
the Casimir energy is exact up to order $a^{-2}m^{-1}$ and contains the
expected divergencies, which can be eliminated using the well established
renormalization procedure for the spherical Casimir effect. The case of a
scalar field present in both the interior and exterior region is also examined
and, for $ma\gg 1$, the zeta function, the Casimir energy, and the Casimir
force are obtained. The obtained Casimir energy and force are exact up to order
$a^{-2}m^{-1}$ and $a^{-3}m^{-1}$ respectively. In this scenario both energy
and force are finite and do not need to be renormalized, and the force is found
to produce an outward pressure on the spherical surface.
