The sinking of flexible mattresses，due to ship movement，water flow，and other factors，is prone to tearing of the mattresses. To explore the influences of relative displacement of the ship，water depth，surface velocity，and arrangement of stiffeners on the forces on downstream sinking flexible mattresses，we build a mathematical model of flexible mattresses according to the catenary theory，and carry out a series of numerical calculations considering the exponential distribution of velocity along water depth. The results show that the relative displacement of the ship，followed by surface velocity and water depth，has the greatest influence on the stresses of flexible mattresses. The maximum axial and transverse stresses are both at the top of the flexible mattresses，and a characteristic of large tensile forces at two ends and small ones in the middle is observed along the mattress width direction. The arrangement of stiffeners can significantly reduce the axial and transverse stresses of the mattresses and thereby prevent the tearing phenomenon.