An upward plane jet impinging on the free surface of a shallow rectangular tank oscillates without any external periodic force. The movement of the impinging point leaves additional fluid mass on the surface behind the point, which does not balance the momentum supplied by the jet. The imbalance generates propagating waves, and a surface level gap appears there. The level gap is flattened not by the waves but by the vertical motion of water columns. The imbalance causes lateral displacement of jet, which in turn causes the imbalance, forming a positive feedback loop. The above model explains well why the frequency corresponds to that of water column oscillation in a partitioned tank with the same water depth, and the oscillation region has a wide range above a certain velocity limit determined by the water depth.