  A measurement of the multi-strange $\Xi^-$ and $\Omega^-$ baryons and their
antiparticles by the ALICE experiment at the CERN Large Hadron Collider (LHC)
is presented for inelastic proton-proton collisions at centre of mass energy of
7 TeV. The transverse momentum ($p_{\rm T}$) distributions were studied at
mid-rapidity (|y| < 0.5) in the range of 0.6 < $p_{\rm T}$ < 8.5 GeV/$c$ for
$\Xi^-$ and $\Xi^+$ baryons, and in the range of 0.8 < $p_{\rm T}$ < 5 GeV/$c$
for $\Omega^-$ and $\Omega^+$. Baryons and antibaryons were measured as
separate particles and we find that the baryon to antibaryon ratio of both
particle species is consistent with unity over the entire range of the
measurement. The statistical precision of the current LHC data has allowed us
to measure a difference between the mean $p_{\rm T}$ of $\Xi^-$ ($\Xi^+$) and
$\Omega^-$ ($\Omega^+$). Particle yields, mean $p_{\rm T}$, and the spectra in
the intermediate $p_{\rm T}$ range are not well described by the PYTHIA Perugia
2011 tune Monte Carlo event generator, which has been tuned to reproduce the
early LHC data. The discrepancy is largest for $\Omega^-$ ($\Omega^+$). This
PYTHIA tune approaches the $p_{\rm T}$ spectra of $\Xi^-$ and $\Xi^+$ baryons
below $p_{\rm T}$ < 0.85 GeV/$c$ and describes the $\Xi^-$ and $\Xi^+$ spectra
above $p_{\rm T}$ > 6.0 GeV/$c$. We also illustrate the difference between the
experimental data and model by comparing the corresponding ratios of
($\Omega^{-}+\Omega^+)/(\Xi^-+\Xi^+)$ as a function of transverse mass.
