A method and apparatus for heating fatty tissue to facilitate liposuction removal of fat, and by additional heating to enable denaturing of the tissue structure. The apparatus uses microwave energy, applied by a cannula (16) to the fatty tissue, as a means to facilitate fat removal. The microwave energy is delivered at a frequency range chosen to optimize energy coupling directly to the fatty tissue, while insuring the attenuation of the radiation level to a safe level in a relatively short distance. The cannula (16) is provided with internal channels to simultaneously provide fluid and remove the mixture of fluid and fatty tissue. Since the microwave frequency is selected to insure direct coupling with the fat tissue, it is not necessary to introduce water to promote coupling, and if water is introduced for cooling or irrigation purposes no salts need to be added to the water for purposes of microwave energy coupling.