  We discuss and compare the effects of one extra dimension in the Randall
Sundrum models on the evaluation of the Casimir force between two parallel
plates. We impose the condition that the result reproduce the experimental
measurements within the known uncertainties in the force and the plate
separation, and get an upper bound kR < 20 if the curvature parameter k of
AdS_5 is equal to the Planck scale. Although the upper bound decreases as k
decreases, kR ~ 12, which is the required value for solving the hierarchy
problem, is consistent with the Casimir force measurements. For the case where
the 5th dimension is infinite, the correction to the Casimir force is very
small and negligible.
