The problem of unsteady flow in the blade passage of a partial admission impulse turbine with supersonic nozzle flow is introduced. Previous work carried out at M.I.T. revealed the presence of a shock wave at the entrance to the blade passages and this report sets out to predict the formation of such a shock wave using a one-dimensional theory. The one-dimensional theory is discussed in some detail and a novel method for dealing with the inflow boundary conditions is developed. Details of a characteristic calculation are given, and this is matched with a shock wave analysis to predict the formation of the shock wave. The implications of the theoretical work are discussed and experimental results obtained from a hydraulic analogy are presented which confirm the analysis.