We present a calculation of the two-graviton exchange contribution to
the law of force between a test mass and a fluctuating mass distributi
on in the limit of targe distances. We find an interaction potential w
hich varies with the distance as R(-7). The effect is suppressed by th
e square of the Planck length Lambda p, so that this gravitational Cas
imir effect is only theoretical, i.e., too small to presently be measu
red.