The conditions for enhancement and inhibition of the spontaneous emiss
ion rate per second by an atom inside coaxial cavities are investigate
d in the electric-dipole approximation. A complete set of vector mode
functions satisfying the boundary conditions is obtained utilizing fie
ld decomposition, which is needed to quantize the electromagnetic held
. The behavior of the emission rate is generally quite complicated; th
ere are sharp peaks at many resonance points, and the minimal values a
pproach unity as the radius of the cavities increases. Emission is usu
ally inhibited completely if the radius is very small. However, under
certain conditions, one being a small radius, there is the possibility
of very large emission due to the TEM mode.