A bumper system includes a tubular beam and a thermoformed energy absorber with crush boxes formed into a base flange, such as by vacuum or thermal forming processes. The crush boxes have planar energy-absorbing sidewalls a depth of about 10 mm to 35 mm, wall thicknesses of about 1 mm to 3 mm, and are formed from polyethylene or other thermoform materials having a memory. The base flange can include thermoformed features engaging recesses in the beam, and is combinable with injection-molded or foam energy absorbers for design flexibility. In one form, the energy absorber includes a thermoformed first sheet forming crush boxes and a second sheet bonded to the first sheet to define apertured air pockets. Related methods of manufacture and impacting are also included.