We present smoothed particle hydrodynamic models of the interactions in the compact galaxy group, Stephan’s Quintet. This work is extension of the earlier collisionless N-body simulations of Renaud et al. in which the large-scale stellar morphology of the group was modelled with a series of galaxy–galaxy interactions in the simulations. Including thermohydrodynamic effects in this work, we further investigate the dynamical interaction history and evolution of the intergalactic gas of Stephan’s Quintet. The major features of the group, such as the extended tidal features and the group-wide shock, enabled us to constrain the models reasonably well, while trying to reproduce multiple features of the system. We found that reconstructing the two long tails extending from NGC 7319 towards NGC 7320c one after the other in two separate encounters is very difficult and unlikely, because the second encounter usually destroys or distorts the already-generated tidal structure. Our models suggest that the two long tails may be formed simultaneously from a single encounter between NGC 7319 and NGC 7320c, resulting in a thinner and denser inner tail than the outer one. The tails then also run parallel to each other as observed. The model results support the idea that the group-wide shock detected in multiwavelength observations between NGC 7319 and NGC 7318b and also the starburst region north of NGC 7318b are triggered by the high-speed collision between NGC 7318b and the intergalactic gas. Our models show that a gas bridge is formed by the high-speed collision and clouds in the bridge continue to interact for some tens of millions of years after the impact. This produces many small shocks in that region, resulting in a much longer cooling time than that of a single impact shock.