The liposuction apparatus (1) comprises in combination a tubular canula (3) having at its distal extremity (18) one or more suction orifices (24) and connected at its proximate extremity (19) to a suction source (14) in communication with these orifices, and a hand piece (2) delivering a spray of working liquid (4) under pressure. The hand piece delivers the spray of liquid under pressure using a conduit opening into an ejection orifice which, when the canula is attached to the hand piece, is located opposite an ejection orifice in the canula located at its distal extremity. A liposuction method using the apparatus is also taught. This invention is of interest to manufacturers and users of surgical equipment.