A linearly actuated pinch clamp is provided, including a housing, a motor connected to the housing, a mechanical drive unit connected to the motor for converting a rotary motion of the motor to a linear motion and for introducing a mechanical advantage to the motion of the motor, and a pinching element having a body and a pinching surface. The pinching element body is coupled to the mechanical drive unit. In certain versions of the pinch clamp, the pinching element is slidably mounted to the housing such that the pinching element is linearly displaceable by the mechanical drive unit between a first position and a second position where the pinching surface cooperates with a fixed surface to pinch closed a flexible tube.