A multi-channel valve apparatus for a multi-channel printhead is provided having ink ports and gas ports defined through a body, first and second pinch elements, and a pinch drive arrangement for selectively moving the first and second pinch elements. Each ink port is configured to receive therethrough a respective one of ink tubes interconnecting ink containers with the printhead. Each gas port is configured to receive therethrough a respective one of gas tubes interconnecting gas vents with the printhead. The first pinch element is moved into and out of pinching contact with the ink tubes so as to respectively block and allow fluid flow through the ink tubes. The second pinch element is moved into and out of pinching contact with the gas tubes so as to respectively block and allow fluid flow through the gas tubes.