Nowadays, advanced surface improvement techniques are required, due to continuously rising demands in aerospace and automotive productions. Laser shock peening (LSP) is a widely known modern surface enhancement method. LSP usually deals with nanosecond laser pulses with high intensities exceeding 1 GW/cm2. Due to very short time scales, all the occurring physical phenomena and processing parameters are extremely difficult to measure and study just based on experimental investigations. Therefore, multidimensional computer simulations of the processes within LSP are required for further optimization. In this work, a 2-D hydrodynamic simulation of water-confined nanosecond laser shock peening of an aluminum target is performed applying the open-source code MULTI2D. Circular laser beam with a pulse energy of 1 J, 20-ns duration, a diameter of 1 mm, and a uniform spatial distribution is used. Spatial profiles of the laser-induced plasma pressure and temperature are determined together with the shock wave parameters. It is shown that the plasma is highly confined and a temperature-affected region is very thin. Radial expansion of the surface pressure profile and the shock wave propagation can be observed, indicating that radial effects have to be considered during the industrial application of LSP. The obtained results are in good agreement with available simulations and measurements, validating the proposed simulation approach. In addition, temporal and spatial distributions of the pressure at the surface of the target material can be applied in finite-element simulations to predict residual stresses distributions.