  The interrogation of an ultra-narrow clock transition of a single trapped ion
for optical frequency metrology requires a laser stabilized to a couple of Hz
per second with a linewidth of the same order of magnitude. Today, lasers in
the visible have reached the Hz-range in frequency stability, if locked onto a
high-finesse, ultra-stable reference cavity. Vertical mounting of the reference
cavity can reduce its sensitivity to vibrations as described in
\cite{notcutt05}. We have designed a comparable vertical cavity with an overall
length of 150 mm resulting in a Free Spectral Range of 1GHz. Optimisation of
the cavity design has been carried out with a Finite-Elements Method, leading
to expected relative length variations below 10$^{-14}$ under the influence of
gravity acceleration (1 $g$). The variation of different geometric parameters
has been studied. The analysis of the different noise sources shows that, for a
regime superior to a tenth of a hertz, the fast linewidth of the laser will not
be limited by the cavity characteristics.
