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Many engineering problems such as exploitation of petroleum and gas, deposition of nuclear waste, and groundwater contamination by organic liquids are closely related to the movement of fluid in rocks. In this paper, a video microscope is employed to investigate the shape of moving front boundary of fluid flow in sandstone. The experimental results show that the fronts of the moving boundary display a fractal behavior. Based on the experimental results, a stochastic differential equation is proposed to describe the moving boundary. By decomposing the velocity of a given point into a drift term and a fluctuation term, the effect of the mesoscope structure of porous media on fluid flow is taken into account. The stochastic approach is in agreement with the experimental results. The analysis shows that the front of the moving boundary of fluid flow in rocks is a comprehensive result caused by the average tendency of fluid flow, which can be described by the classical Darcys Law, and the fluctuation tendency of fluid flow, which is closely related to the mesoscope structure of rocks.