When a load is applied to a free surface of cohesive fine powder in a vessel, the powder can spurt from a small orifice, which we call the flushing. A gas-solid two-phase flow model using Darcy's law examines this phenomenon. The numerical simulation by this model is qualitatively verified by the measurement for a case when the powder in a rectangular vessel spurts from a slit by a constant piston load. It is found that near the slit, there appears a high-speed region of particle of which velocity is considerably larger than that of free-flowing due to the gravity.