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It is shown that the equation which describes constant mean curvature surfaces via the generalized Weierstrass-Enneper inducing has Hamiltonian form. Its simplest finite-dimensional reduction is the integrable Hamiltonian system with two degrees of freedom. This finite-dimensional system admits S 1 -action and classes of S 1 -equivalence of its trajectories are in one-to-one correspondence with different helicoidal constant mean curvature surfaces. Thus the interpretaion of well-known Delaunay and do Carmo-Dajzcer surfaces via integrable finite-dimensional Hamiltonian system is established.Surfaces, interfaces, fronts, and their dynamics are key ingredients in a number of interesting phenomena in physics. They are surface waves, growth of crystal, deformation of membranes, propagation of flame fronts, many problems of hydrodynamics connected with motion of boundaries between regions of differ densities and viscosities (see, e.g., [1,2]). Quantum field theory and statistical physics are the important customers of surfaces too (see [3,4]).Mean curvature plays special role among the characteristics of surfaces and their dynamics in several problems both in physics and mathematics (see, e.g., [5,6]). Surfaces of constant mean curvature have been studied intensively during last years (see, e.g., [7,8,9]).

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