Bare, cylindrical, explosive charges produce secondary shock waves in the direction of least presented area. Whilst the source of these shock waves was explored in the 1940's, no attempt was made to predict them. This paper describes the detonation of bare, cylindrical charges of PE4 (RDX binder 88/12%), mass 0.2 to 0.46kg and with a length to diameter ratio of 4 to 1. High speed camera footage showed (i) the formation of the separate, primary, shock waves from the sides and ends of the charge, (ii) Mach reflection of these separate shock waves, giving rise to reflected, secondary shock waves, and (iii) the secondary shock waves catching and merging with the primary shock wave. In the axial direction, the secondary shock wave's peak overpressure and impulse exceeded that of the primary shock wave for scaled distances, Z=R/M-1/3 3.9mkg(-1/3), where M is the mass in kg and R the distance from the charge in m. It was found possible to predict the primary peak overpressure, P, at all distances in the axial direction, for a constant length to diameter ratio, using P=3075Z(-3)-1732Z(-2)+305Z(-1). Close in the primary peak overpressure is proportional to M/R-3 in the axial direction. It was not possible to predict the secondary peak overpressure with the data obtained. The total impulse from both shock waves, I, in the axial direction can be predicted using I=746(M-2/3/R)(3)-708(M-2/3/R)(2)+306(M-2/3/R).