Phenomenological Lagrangians for physical systems with spontaneously broken symmetries are reformulated in terms of gauge field theory. Description of the Dirac p-branes in terms of the Yang-Mills-Cartan gauge multiplets interacting with gravity, is proved to be equivalent to their description as a closed dynamical system with the symmetry ISO(1, D - 1) spontaneously broken to ISO(1,p) x SO(D - p - 1).