Observed galaxy clusters often exhibit X-ray morphologies suggestive of recent interaction with an infalling subcluster. A3376 is a nearby (z = 0.046) massive galaxy cluster whose bullet-shaped X-ray emission indicates that it may have undergone a recent collision. It displays a pair of Mpc-scale radio relics and its brightest cluster galaxy is located 970 h− 170 kpc away from the peak of X-ray emission, where the second brightest galaxy lies. We attempt to recover the dynamical history of A3376. We perform a set of N-body adiabatic hydrodynamical simulations using the smoothed particle hydrodynamics (SPH) code gadget-2. These simulations of binary cluster collisions are aimed at exploring the parameter space of possible initial configurations. By attempting to match X-ray morphology, temperature, virial mass and X-ray luminosity, we set approximate constraints on some merger parameters. Our best models suggest a collision of clusters with mass ratio in the range 1/6–1/8, and having a subcluster with central gas density four times higher than that of the major cluster. Models with small impact parameter (b < 150 kpc), if any, are preferred. We estimate that A3376 is observed approximately 0.5 Gyr after core passage, and that the collision axis is inclined by i ≈ 40° with respect to the plane of the sky. The infalling subcluster drives a supersonic shock wave that propagates at almost 2600 km s−1, implying a Mach number as high as |$\mathcal {M}\sim 4$|; but we show how it would have been underestimated as |$\mathcal {M}\sim 3$| due to projection effects.