Although predicted early in the 20th century, a single-phase vapour rarefaction shock wave has yet to be demonstrated experimentally. Results from a previous shock tube experiment appear to indicate a rarefaction shock wave. These results are discussed and their interpretation challenged. In preparation for a new shock tube experiment, a global theory is developed, utilizing a van der Waals fluid, for demonstrating a single-phase vapour rarefaction shock wave in the incident flow of the shock tube. The flow consists of four uniform regions separated by three constant-speed discontinuities: a rarefaction shock, a compression shock, and a contact surface. Entropy jumps and upstream supersonic Mach number conditions are verified for both shock waves. The conceptual van der Waals model is applied to the fluid perfluoro-tripentylamine (FC-70, C15F33N) analytically, and verified with computational simulations. The analysis predicts a small region of initial states that may be used to unequivocally demonstrate the existence of a single-phase vapour rarefaction shock wave. Simulation results in the form of representative sets of thermodynamic state data (pressure, density, Mach number, and fundamental derivative of gas dynamics) are presented.