The expansion of plasma plume produced by a laser ablation is investigated using the self-similar approach. Based on the fluid model and the quasi-neutral assumption, the one dimensional expansion of an either vapor or partially ionized gas is studied for a collisionless plasma in the presence of electrons in thermal equilibrium. The uniqueness of the self-similar solution is questioned. Two different self-similar transformations for the ion density are proposed, one commonly used for free plasma expansion and the other corresponds to the expansion with diffusion. The density profiles and the self-similar parameter limit, corresponding to the end of the expansion, are found to be strongly affected by the transformation. A comparison is made with experimental results of a plasma produced by nanosecond laser pulse interacting with a metallic titanium target in a vacuum.© (2010) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.