  We evaluate the Casimir force between two parallel plates in Randall Sundrum
(RS) scenarios extended by q compact dimensions. After giving exact expressions
for one extra compact dimension (RS 6D model), we generalize to an arbitrary
number of compact dimensions. We present the complete calculation for both two
brane scenario (RSI model) and one brane scenario (RSII models) using the
method of summing over the modes. We investigate the effects of extra
dimensions on the magnitude and sign of the force, and comment on limits for
the size and number of the extra dimensions.
