A theoretical development is described whereby cylindrically symmetric flows involving multiple shock waves may be mapped in both time and space. The theory is an extension of earlier work by Dewey which was restricted to flows with spherical symmetry and in which only one shock wave was present. The method requires a knowledge of the trajectories of individual air elements from which the density can be calculated by using the Lagrangian form of the equation of continuity. The other thermodynamic variables can be derived by assuming that, except in the shock waves, the flow is reversible and adiabatic. The theory has been applied to an investigation of the flow field associated with the explosion of 479 kg of TNT placed 22 m above the ground surface. The flow field is spherically symmetric until the initial shock wave is reflected from the ground after which it is symmetrical in azimuth but not in elevation. The presence of the reflected shock wave introduces a second shock wave into the problem which must be included in the analysis in order to obtain a complete description of the flow. The particle trajectories were obtained by using an array of smoke puffs whose motions were followed photographically. The results obtained by analysing the particle trajectories by the theoretical approach described in this paper have been compared with the results obtained from piezo-electric pressure transducers at several points in the flow field and strikingly good correlation has been noted. A brief discussion is included on the effects of certain simplifications introduced into the analysis for reasons of practical convenience. It has been concluded that the theory proposed is a valid one having general application to situations where gasdynamic effects are preponderant.