This paper presents theoretical work on the wave motion in an elliptical water jet generator. Such a device consists of a water filled elliptical cavity in which a shock wave is induced at one focus by a spark discharge. The shock converges to the other focus and via a convergent duct is allowed to reflect off a free surface of the liquid at the front of a nozzle, whereby a jet is emitted. The initial value problem of how a weak shock develops and how it is reflected from the walls of a cavity with small eccentricity is studied by using acoustic theory and a perturbation technique. In order to account for the distensibility of the wall material its admittance is introduced as a parameter. The validity of the results is extended to larger eccentricities by use of Padé approximants and by comparison with a geometrical acoustics solution to the same problem. The implications of the results on the design of the water jet generator are indicated.