The dynamics of a laser ablation plume during the first stage of its expansion, just after the termination of the laser pulse is modelled. The one-dimensional expansion of the evaporated material, considered as an ideal fluid, is governed by one-fluid Euler equations. For high energetic ions, the charge separation can be neglected and the hydrodynamics equations solved using self-similar formulation. Numerical solution is obtained, first when the laser fluence range is low enough to deal with a neutral vapor, and in a second stage, when ionization effects on the expansion are taken into account, for different material targets. As a main result, we found that the presence of ions in the evaporated gas enhances the self-similar expansion. (C) 2008 Elsevier B. V. All rights reserved.