Abstract: Laser-driven reservoir can be used to generate quasi-isentropic compression. In this paper, a method is proposed to estimate the pressure at the front of the sample. When laser-driven shock wave relaxes after reaching the rear surface of reservoir, the generated plasma expands in the vacuum, and ultimately piles up at the front of the sample with low pressure and temperature, and in time period longer than that without vacuum. Assuming the unloading reservoir as a poly-tropic gas, and dividing it into several layers, the analytic self-similar solution is obtained for every layer to describe the velocity, pressure, and density of the plasma expansion into the vacuum. With the solutions, a computation code is given to calculate the time dependent pressure. Compared with the experimental back integrated results, the simplified model is reasonable to estimate pressure at the front of the sample.