The invention provides a surgical electrocautery method and apparatus that achieves sealing along the entire tissue length, and that also is able to deliver adequate force to produce an effective electrocautery seal. This problem is solved by using an incompressible fluid contained in a sac or sacs positioned to support the one or more electrodes used for electrocauterization. The profile of the electrodes thus conforms to the tissue surface and thickness variations, while exerting an optimized pressure along the entire length of the surface.