The one-dimensional hydrodynamic expansion of plasmas produced by laser beams focused on thin foil targets is studied by using a self-similar approach. This work is an extension of the London and Rosen model proposed in the context of x-ray laser studies. Here, cases with non-flat-top laser pulses are considered and, for some of these, an exact analytic solution is deduced. The model is useful to study long scale length plasmas, produced by uniform laser irradiation, which become fully underdense during the laser pulse. It predicts the fundamental plasma variables (scale lengths, density, temperature) as a function of the experimental parameters (laser intensity, wavelength and pulse duration, target thickness and composition).