  The dynamics of superconductivity phase in thick stack of Josephson junctions
with strong inductive coupling, such as the one realized in layered high-$T_c$
cuprates and possibly the recently discovered FeAs-based superconductors, is
investigated under a c-axis bias voltage and in the absence of an external
magnetic field. The kink state found previously by the present authors is
extended to three dimensions for both rectangular and cylindrical geometries.
The IV characteristics are calculated and the distributions of electromagnetic
field inside the samples are clarified. The solution for a cylindrical mesa
exhibits a higher resonating frequency than that of a square mesa with the same
linear size by a factor of $\sim 2.4$. More importantly, from the radius
dependence of the resonance frequency for the cylinder geometry it is possible
to confirm directly the kink state, and thus to reveal the mechanism of the
strong radiation discovered in recent experiments.
