A traveling wave air mattress apparatus includes an air mattress comprised of an 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 sequences of the air bladder cells timed sequences of air pressure pulses which vary pressures in the cells from quiescent pressures, the air pressure variations resulting in leading and lagging soliton-like traveling waves of body support force variation which travel longitudinally over the surfaces of the pulsed air bladder cells, thus inhibiting formation of bedsores. The wave patterns may optionally simulate water waves and/or rocking motions of a boat to produce relaxing effects.