The physical phenomena involved in the interaction of a laser-generated plasma plume with a background gas are studied numerically. A three-dimensional combined model is developed to describe the plasma plume formation and its expansion in vacuum or into a background gas. The proposed approach takes advantages of both continuous and microscopic descriptions. The simulation technique is suitable for the simulation of high-rate laser ablation for a wide range of background pressure. The model takes into account the mass diffusion and the energy exchange between the ablated and background species, as well as the collective motion of the ablated species and the background-gas particles. The developed approach is used to investigate the influence of the background gas on the expansion dynamics of the plume obtained during the laser ablation of aluminum. At moderate pressures, both plume and gas compressions are weak and the process is mainly governed by the diffusive mixing. At higher pressures, the interaction is determined by the plume-gas pressure interplay, the plume front is strongly compressed, and its center exhibits oscillations. In this case, the snowplough effect takes place, leading to the formation of a compressed gas layer in front of the plume. The background pressure needed for the beginning of the snowplough effect is determined from the plume and gas density profiles obtained at various pressures. Simulation results are compared with experimentally measured density distributions. It is shown that the calculations suggest localized formation of molecules during reactive laser ablation.