The von Neumann three‐shock theory does not adequately describe the conditions close to the triple point of the Mach reflection of weak shocks (M<1.5), and produces no solution for incident shocks with a Mach number less than about 1.25 in air. Experimental evidence, on the other hand, indicates that reflection does occur under these conditions, and it is suggested that the discrepancy is because the von Neumann theory assumes that the reflected and Mach stem shocks are plane oblique shocks bounding regions with uniform properties. In practice, the reflected shock and Mach stem are curved oblique shocks which bound regions with transverse gradients in their physical properties. The physical behind these shocks can be measured using infinite fringe interferometry. Alternatively, it will be shown that the physical properties behind these curved shocks can be determined from a shadow or schlieren photograph which gives information only about the position and shape of the shocks. The experimental observations suggest that the Mach stem and reflected shock in the region close to the triple point are approximately circular in cross section. Assuming circularity of the reflected and Mach stem shocks permits a determination of the angles between the shocks at the triple point and these, together with the observed triple point trajectory angle, can be used in a modified oblique shock solution which agrees with the experimental observations, if the condition for parallel flow on the two sides of the contact surface is relaxed. The shock polar representation of this solution is illustrated. It is concluded that Mach reflection of shocks with Mach numbers in the range 1.1<M<1.25 is possible, but the simple three shock theory is invalid.