  A study of various SUSY scenarios is presented in which the lightest
supersymmetric particle is the gravitino $\sG$ and the next-to-lightest
supersymmetric particle is a scalar tau $\stau$ with lifetimes ranging from
seconds to years. Gravitinos are interesting dark matter candidates which can
be produced in decays of heavier sparticles at the International Linear
Collider (ILC), but remain undetected in direct searches of astrophysical
experiments. We investigate the detection and measurement of metastable staus,
which may be copiously produced at the ILC either directly or via cascade
decays. A proper choice of the experimental conditions will allow one to stop
large samples of staus in the calorimeters of the ILC detector and to study the
subsequent decays $\stau\to\tau\sG$. Detailed simulations show that the
properties of the stau and the gravitino, such as stau mass and lifetime and
gravitino mass, can be accurately determined at a future ILC and may provide
direct access to the gravitational coupling, respectively Planck scale.
