Pinch clamps are provided which generate positive displacement while also preventing rebound. To prevent rebound while providing positive displacement, the upper and lower clamping surfaces may be configured to form a pinch profile along which the tubing is compressed with the pinch point being formed at the distal end of the pinch profile. To further prevent rebound, the lower arm of the pinch clamp can include blocking ribs that interface with the upper clamping surface to prevent distal travelling of the pinch point even if the upper arm is forced into an over-engaged position.