When a nanosecond laser pulse hits a 250 µm thick Al target in the presence of a confinement medium, the plasma expansion generates a mechanical shock wave, which then travels through the solid bouncing numerous times back and forth between the free surfaces of the sample. The time interval corresponding to the first few hundreds of ns has been extensively studied, providing an experimental layout for implementation of dynamic constitutive laws and damage criteria of materials. The final deformation of thin samples produced by laser shock showed the possibility of using this technique for the shaping of metals in highly dynamic conditions. This new opportunity could open in the future to innovative industrial applications. This study focused on the long-term effects (i.e. few µs), responsible for the final deformation observed in the Al sheets. High resolution velocity measurements were performed by VISAR (Velocity Interferometer System for Any Reflector) during the laser shock experiments. Their comparison with 1D and 2D numerical simulations of the mechanical shock wave propagation showed that the classical exponential decaying pressure loading, used to model the laser-matter interaction in this domain, was not suitable to explain the experimental data. The role of the material model and its parameters was also evidenced as a moderate possible explanation of the discrepancy between simulations and experiments. Conversely, the simulations showed that the residual deformation of Al under laser shock and the overall free surface velocity experimental measurement is mostly dependent on the plasma release modeling of the loading as represented by the decay of the laser loading. This study gives new insights in the interpretation of laser-matter interaction and the modeling of laser-induced mechanical shocks in solids below their damage threshold with possible applications in dynamic forming of materials.