  We study the hierarchy problem on the four- and five-branes which are
constructed by attaching a circle and a sphere to the standard three-brane,
respectively. The effective masses in their excited spectra on these extended
dimensional branes imply intriguing characteristics associated with the
quantization of the compact circular and spherical manifolds. In particular,
their lightest effective masses are shown to suppress exponentially with
respective to the Planck mass, similar to the three-brane case. We also
investigate the effective couplings in these extended dimensional branes.
