A bumper system includes primary and secondary structural cross beams, at least one having an S-shaped cross section with forwardly-facing (or outwardly-facing) top concavity. The beams include different arrangements of stiffening ribs in concavities formed by the S-shaped cross section for impact and bending strength. In one form, the beams are made of polymeric material. The beams may include integrally formed crush cans for attachment to the vehicle frame, or alternatively can be attached to vehicle frame rail tips by separate metal crush cans and brackets.
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