A lateral displacement shock absorbing material includes a material consisting of elongated tubular impact absorbing members, each having an axis of elongation. The axes of elongation are parallel to one another by virtue of lateral webbing interconnecting them together. Each of the tubular members has an outer surface made up of two frustoconical surfaces with their larger diameter ends abutting one another and their smaller diameter ends facing away from one another. Each tubular member includes a passageway defined by two frustoconical shapes with the smaller diameter ends abutting one another, and the larger diameter ends facing away from one another and defining the openings of each passageway. Upon impact, the side walls of the tubular members bulge or displace laterally to absorb impacts.