An air mattress apparatus includes an air mattress which comprised of an array of air bladder cells that are individually inflatable to quiescent pressure levels which provide comfortable support for the body of a human, and a pressure-pulse generator controlled by a wave sequence generator for introducing into ordered patterns of air bladder cells a wave-like time sequence of air pressure pulses which vary quiescent pressure levels in the cells, the pressure wave resulting in a traveling wave of support force variation which travels 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.