A OD numerical approach including a Collisional-Radiative model is elaborated in the purpose of describing the behavior of the nascent plasma resulting from the interaction between a laser pulse (lambda = 532 nm, tau = 4 ns and F = 6.5 J cm(-2)) with an aluminum sample. The species considered are Al, Al+, Al2+ and Al3+ on their different excited states and free electrons. Both groups of particles are characterized by their translation temperature in thermal non-equilibrium state. Besides, each population density is assumed to be in chemical non-equilibrium and behaves freely through the seven involved elementary processes (electron impact induced excitation and ionization, elastic collisions, multi-photon ionization, inverse laser Bremsstrahlung, direct electron Bremsstrahlung and spontaneous emission). Atoms passing from sample to gas phase are described by considering classical vaporization phenomena so that the surface temperature is limited to values less than the critical point. The relative role of the elementary processes is discussed and the time-evolution of the excitation of the species is analyzed.