A recoiling energy absorbing system has an upper impact surface that is exposed to percussive impact. An energy absorbing layer is positioned below or inside the upper impact surface. The energy absorbing layer includes one or more thermoformed energy absorbing modules. At least some of the modules are provided with one or more energy absorbing units that extend from an upper platform. Several of the energy absorbing units are provided with a flexible wall that extends from the upper platform. A lateral reinforcement member secures the energy absorbing units to prevent them from splaying. The energy absorbing units at least partially absorb energy generated by an impacting object due to the flexible wall bending inwardly or outwardly and recoiling nondestructively after single or multiple impacts to its un-deflected configuration.