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