Vibration phenomena associated with narrow channel flow have come under study as a result of the core failure of an early nuclear rocket engine. Since the mechanism of this vibration instability was not well understood at the time of failure, an investigation of a simple system consisting of a rigid plate with two degrees of spring-restrained freedom in a two-dimensional channel has been made both experimentally and analytically. The results show a strong dependence of the flow rate required for plate oscillation on the channel width (normal to plate).