In order to control laser-induced shock processes, two main points of interest must be fully understood: the laser–matter interaction generating a pressure loading from a given laser intensity profile and the propagation of induced shock waves within the target. This work aims to build a predictive model for laser shock-wave experiments with two grades of aluminum at low to middle intensities (50 to ) using the hydrodynamic Esther code. This one-dimensional Lagrangian code manages both laser–matter interaction and shocks propagation. The numerical results are compared to recent experiments conducted on the transportable laser shocks generator facility. The results of this work motivate a discussion on the shock behavior dependence to elastoplasticity and fracturation models. Numerical results of the rear surface velocity show a good agreement with the experimental results, and it appears that the response of the material to the propagating shock is well predicted. The Esther code associated to this developed model can therefore be considered as a reliable predictive code for laser ablation and shock-wave experiments with pure aluminum and 6061 aluminum in the mentioned range of parameters. The pressure–intensity relationship generated by the Esther code is compared to previously established relationships.