As a kind of rapid filling hydraulic structure, geomembrane tube can effectively act as flood barriers and cofferdams for flood risk management. L-shaped block is used to support geomembrane tube to prevent it from rolling. The contact force between the L-shaped block and the geomembrane tube is analyzed by using particle flow code (PFC2D) software, and the overturning stability of the L-shaped block is calculated. The relationship between the key factors and the overturning stability was established. It is found that the central angle of the L-shaped block has little influence on the overturning stability. The overturning stability decreases with the increase of the initial pumping pressure. Keeping Lw/Lb unchanged, increasing Lb will improve the overturning stability where Lw and Lb are the width and the height of the Lshaped block. Under the ultimate water level, when 1.23 Lbcr < Lw≤1.55 Lbcr, the L-shaped block is in the state of overturning stability where Lbcr is the critical height of the L-shaped block. The initial pumping pressure is less than 0.152γL, the L-shaped block is in the state of overturning stability with Lw/Lbcr =1.0 where L is the cross-sectional perimeter of the geomembrane tube and γ is the unit weight of the filling liquid, on the contrary, Lw/Lbcr must be greater than 1 to ensure its overturning stability.