A tissue treatment apparatus and method are provided for treating tissue by the application of the time-varying sub-atmospheric pressure. The apparatus includes a cover adapted to cover a wound and adapted to maintain sub-atmospheric pressure the site of the wound. The apparatus further includes a source of suction configured to generate a time-varying sub-atmospheric pressure having a periodic waveform comprising a gradual change in pressure. The suction source cooperates with the cover to supply the time-varying sub-atmospheric pressure under the cover to the wound. The time-varying sub-atmospheric pressure may vary between a first pressure value below the inherent tissue tension of the wound tissue and a second pressure value above the inherent tissue tension of the wound tissue.