A traveling wave air mattress apparatus includes an air mattress comprised of a array of laterally disposed, longitudinally spaced air bladder cells that are individually inflatable to quiescent pressure levels which provide comfortable support for a human body, and an air pressure-pulse generator controlled by a wave sequence generator for periodically introducing into a sequence of the air bladder cells a time sequence of air pressure pulses which vary pressures in the cells from quiescent pressures, the air pressure variations resulting in a soliton-like traveling wave of body support force variation which travels longitudinally over the surfaces of the pulsed air bladder cells, thus inhibiting formation of bedsores. The wave pattern may optionally simulate water waves and/or rocking motions of a boat to produce relaxing effects.