Optimization of the laser shock peening (LSP) and LASer Adhesion Test (LASAT) processes requires control of the laser-induced target's loading. Improvements to optical and laser technologies allow plasma characterization to be performed with greater precision than 20 years ago. Consequently, the processes involved during laser-matter interactions can be better understood. For the purposes of this paper, a self-consistent model of plasma pressure versus time is required. The current approach is called the inverse method, since it is adjusted until the simulated free surface velocity (FSV) corresponds to the experimental velocity. Thus, it is not possible to predict the behavior of the target under shock without having done the experiments. For the first time, experimental data collected in different labs with the most up-to-date laser parameters are used to validate a self-consistent model for temporal pressure-profile calculation. In addition, the parameters characterizing the plasma (temperature, thickness and duration) are obtained from the ESTHER numerical code, together with the amount of ablated matter. Finally, analytic fits are presented that can reproduce any pressure-temporal profiles in the following domains of validity: Intensities, I, ranging from 10 to 500 GW cm-2 and pulse durations, T pul, between 5 and 40 ns for the direct-illumination regime at 1053 nm, I ranging from 1 to 6 GW cm-2 and T pul between 10 to 40 ns in the water-confined regime at 1053 nm, and I from 1 to 10 GW cm-2 and T pul between 7 and 20 ns in the water-confined regime at 532 nm. These temporal pressure profiles can then be used to predict the aluminum target's behavior under laser shock using mechanical simulation software.