An experimental, numerical, and analytical study of the acceleration and deceleration process of thin metallic foils immersed in water and submitted to laser driven shocks is presented. Aluminum and copper foils of 20 to 120 mu m thickness, confined on both sides by water, have been irradiated at 1.06 mu m wavelength by laser pulses of similar to 20 ns duration, similar to 17 J energy, and similar to 4 GW/cm(2) incident intensity. Time resolved velocity measurements have been made, using an electromagnetic velocity gauge. The recorded velocity profiles reveal an acceleration-deceleration process, with a peak velocity up to 650 m/s. Predicted profiles from numerical simulations reproduce all experimental features, such as wave reverberations, rate of increase and decrease of velocity, peak velocity, effects of nature, and thickness of the foils. A shock pressure of about 2.5 GPa is inferred from the velocity measurements. Experimental points on the evolution of plasma pressure are derived from the measurements of peak velocities. An analytical description of the acceleration-deceleration process, involving multiple shock and release waves reflecting on both sides of the foils, is presented. The space-time diagrams of waves propagation and the successive pressure-particle velocity states are determined, from which theoretical velocity profiles are constructed. All characteristics of experimental records and numerical simulations are well reproduced. The role of foil nature and thickness, in relation with the shock impedance of the materials, appears explicitly. (C) 1997 American Institute of Physics.