  We present an X-ray spectral analysis of the nearby double radio relic
merging cluster Abell 3376 ($z$ = 0.046), observed with the $Suzaku$ XIS
instrument. These deep ($\sim$360 ks) observations cover the entire double
relic region in the outskirts of the cluster. These diffuse radio structures
are amongst the largest and arc-shaped relics observed in combination with
large-scale X-ray shocks in a merging cluster. We confirm the presence of a
stronger shock (${\cal M}_{\rm{W}}$ = 2.8 $\pm~0.4$) in the western direction
at $r\sim26$', derived from a temperature and surface brightness discontinuity
across the radio relic. In the East, we detect a weaker shock (${\cal
M}_{\rm{E}}$ = 1.5 $\pm~0.1$) at $r\sim8$', possibly associated to the 'notch'
of eastern relic, and a cold front at $r\sim3$'. Based on the shock speed
calculated from the Mach numbers, we estimate that the dynamical age of the
shock front is $\sim$0.6 Gyr after core passage, indicating that Abell 3376 is
still an evolving merging cluster and that the merger is taking place close to
the plane of the sky. These results are consistent with simulations and optical
and weak lensing studies from the literature.
