  The structure and evolution of the stellar velocity ellipsoid plays an
important role in shaping galaxies undergoing bar driven secular evolution and
the eventual formation of a boxy/peanut bulge such as present in the Milky Way.
Using collisionless N-body simulations, we show that during the formation of
such a boxy/peanut bulge, the meridional shear stress of stars, which can be
measured by the meridional tilt of the velocity ellipsoid, reaches a
characteristic peak in its time evolution. It is shown that the onset of a bar
buckling instability is closely connected to the maximum meridional tilt of the
stellar velocity ellipsoid. Our findings bring new insight to this complex
gravitational instability of the bar which complements the buckling instability
studies based on orbital models. We briefly discuss the observed diagnostics of
the stellar velocity ellipsoid during such a phenomenon.
