This work is concerned with the study of the important physical processes present in a laser ablation lithium plasma plume expanding into vacuum. A numerical model has been developed encompassing three main areas, namely, hydrodynamics, atomic physics and radiative transfer and spectroscopy. A self-similar expansion model has been employed to study the hydrodynamics. A comparison between the isothermal and lsentropic self-similar solutions has been performed over a wide range of experimental initial conditions with varying fluence, laser wavelength and target spot size. The effect of these variations is seen, where one of these models predicts experimental observations more accurately, depending on the initial conditions present. Both models have been modified to include the bulk motion of the plasma by considering the pressure exerted by the expanding plume onto the target. The steady state colhsional radiative model was used to calculate the electron, ion and energy level populations of lithium neutral in the expanding plume and is used as a post-processor to the hydrodynamics model. The validity conditions of various equilibrium models and steady state conditions have been assessed, with particular emphasis on the spatial and temporal regions applicable to local thermodynamic equilibrium (LTE). The information taken from the first two models allows the calculation of the full radiative transfer equation through plasma chords parallel to the target surface. Results from this calculation have been compared with experimental timeintegrated spectra. This model was also used to explain a well-known anomalous line intensity ratio between two strong emission lines m neutral lithium produced in a laser ablation plasma.