Determining the instant for support activation in plane strain tunnel calculations is an essential step, as for Convergence Confinement Method. Recent researches on that subject lead to an original development of that Method which allows for an accurate determination of that instant. The proposed methodology results from "experimental numerical laws" learned from comparison between plane strain approach and direct three dimensional one. For this purpose, a reference three dimensional geometry is considered: a constant rate advancing circular tunnel in anisotropic geostatic stress state, with one principal direction parallel to tunnel axis. The isotropic state of stress is first considered. It is shown that two fundamental principles allow to treat completely the plane strain approach. It is then shown how these principles can be extended to the anisotropic stress state, using a "mean convergence curve concept Finally, it is proposed to apply such a method to three dimensional tunnels in steady state advancement. With such improvements, the Convergence Confinement Method appears as a self-contained plane strain approach to the three dimensional advancing tunnel problem, without much additional intricacy to classical approaches.