  Casimir energy is calculated in the 5D warped system. It is compared with the
flat one. The position/ momentum propagator is exploited. A new regularization,
called {\it sphere lattice regularization}, is introduced. It is a direct
realization of the geometrical interpretation of the renormalization group. The
regularized configuration is closed-string like. We do {\it not} take the
KK-expansion approach. Instead the P/M propagator is exploited, combined with
the heat-kernel method. All expressions are closed-form (not KK-expanded form).
Rigorous quantities are only treated (non-perturbative treatment). The properly
regularized form of Casimir energy, is expressed in the closed form. We
numerically evaluate its $\La$(4D UV-cutoff), $\om$(5D bulk curvature,
warpedness parameter) and $T$(extra space IR parameter) dependence.
