Expansion Deflection (ED) nozzles have long been considered as an alternative to conventional bell and conical designs. The ED nozzle has two primary benefits over such nozzle configurations, being shorter, and with the potential for altitude compensation. However, the difficulties involved with modelling the complex flow interactions within the nozzle type have thus far prevented the creation of a reliable method for its design and analysis. The work presented within this dissertation makes use of a combination of several different approaches to flow solution to provide a more complete analysis than previously achieved. The primary advance is the use of a CFD scheme to analyse the transonic throat region, the results of which are used as input to a Method of Characteristics based algorithm for the solution of the inviscid supersonic flow-field. This method is both efficient, and allows contour optimisation through the calculus of variations. The viscous flow region is treated in a partially or fully empirical manner, depending upon ambient pressure. The results of this analysis reveal several previously unidentified flow-field behaviours and design parameter interactions. Careful selection of the variables used to define the throat region is shown to be of considerable importance, as they effect not just the thrust produced, but also whether a real flow through such a nozzle may' exist. Secondly, the high probability of shock wave formation and interaction with the nozzle wall within length optimised ED nozzles is demonstrated. This has consequences for both the design and analysis of the ED nozzle. Overall, a framework is established which allows the flow behaviour and performance characteristics of the nozzle type to be estimated in greater detail than previously possible. The performance increments demonstrated over conventional bell nozzles include an approximately 25 to 50 percent length reduction for nozzles designed for solely high altitude operation, and a similar reduction in length plus a noticeable increase in low altitude thrust for trans-atmospheric nozzles. However, before application of the ED nozzle concept to a real system becomes possible, several areas of uncertainty must be addressed, and these are highlighted at the end of this dissertation.