  The pressure dependence of phase transitions in the quasi one-dimensional
vanadium oxide $\beta$-Na$_{1/3}$V$_2$O$_5$ has been studied by magnetic
susceptibility and electrical resistivity measurements. The pressure dependence
of the various transition temperatures is quite differently. The transition at
T=240 K, previously reported and attributed to ordering on Na sites, and a
second transition at $T \approx 222$ K, reported here for the first time and
attributed to a further increase of order on Na sites, are almost independent
of pressure. On the other hand, the metal-insulator (MI) transition at
$T_{MI}=130$ K shifts to lower temperatures, while the magnetic transition at
$T_N=24$ K shifts to higher temperatures with increasing pressure. We discuss
the different pressure dependencies of $T_{MI}$ and $T_N$ in terms of
increasing interchain coupling and the MI transition to be of Peierls type.
