This study investigates the transient loading exerted on rigid circular cylinders by impinging pressure waves of arbitrary shape, amplitude, and time duration. Numerical calculations are used to predict the transient flow around the cylinder for wide ranges of geometric and loading parameters. An analytical model is developed to predict the transient loading history on the cylinder and this is found in good agreement with the results of the numerical calculations. Both models are used to identify and explore the different loading regimes, and to construct non16 dimensional maps to allow direct application of the findings of this study to the design of structures exposed to the threat of pressure wave loading.