A lateral displacement shock absorbing material includes a material consisting of a plurality of elongated tubular impact absorbing members, each having an axis of elongation. The axes of elongation of the respective tubular members are parallel to one another. The tubular members are retained with their axes in parallel relation by virtue of webbing, laterally extending from the sides of each tubular member, and interconnecting them together. Each of the tubular members consists of 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. The material may be made of thermoplastics including polypropylene, urethanes, and rubber. In operation, upon impact, the side walls of the tubular members bulge or displace laterally to absorb impacts. The taper of the walls and the open space within the tubular members allow the energy absorbing material to displace laterally allowing a greater range of travel.