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We present an X-ray spectral analysis of the nearby double radio relicmerging cluster Abell 3376 ($z$ = 0.046), observed with the $Suzaku$ XISinstrument. These deep ($\sim$360 ks) observations cover the entire doublerelic region in the outskirts of the cluster. These diffuse radio structuresare amongst the largest and arc-shaped relics observed in combination withlarge-scale X-ray shocks in a merging cluster. We confirm the presence of astronger shock (${\cal M}_{\rm{W}}$ = 2.8 $\pm~0.4$) in the western directionat $r\sim26$', derived from a temperature and surface brightness discontinuityacross the radio relic. In the East, we detect a weaker shock (${\calM}_{\rm{E}}$ = 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 speedcalculated from the Mach numbers, we estimate that the dynamical age of theshock front is $\sim$0.6 Gyr after core passage, indicating that Abell 3376 isstill an evolving merging cluster and that the merger is taking place close tothe plane of the sky. These results are consistent with simulations and opticaland weak lensing studies from the literature.

X-ray study of the double radio relic Abell 3376 with Suzaku