  We study the dynamics of the Nambu-Goto membranes with cohomogeneity one
symmetry, i.e., the membranes whose trajectories are foliated by homogeneous
surfaces. It is shown that the equation of motion reduces to a geodesic
equation on a certain manifold, which is constructed from the original
spacetime and Killing vector fields thereon. A general method is presented for
classifying the symmetry of cohomogeneity one membranes in a given spacetime.
The classification is completely carried out in Minkowski spacetime. We analyze
one of the obtained classes in depth and derive an exact solution.
