Shock waves are known to display structure within their fronts. At lower stress amplitudes, elastic waves precede an inelastic rise to the final pressure whilst under more extreme loading there is a single inelastic shock to peak stress. These regimes are conventionally termed weak and strong shock behaviour and the transition stress between the two is called the weak shock limit (WSL) here. Shock speeds in an amorphous glass and a FCC metal are shown to change discontinuously as pulses of increasing peak pressure exceed this limit. Further this work correlates the stress at the WSL with the theoretical strength of ca. 40 solids and shows different dependence for close-packed and open structures in metals, polymers, ceramics, and ionic solids. (c) 2014 AIP Publishing LLC.