The scattering of fast charged particles in a bent crystal has been analyzed in the framework of relativistic classical mechanics. The expressions obtained for the deflection function are in satisfactory agreement with the experimental data for the volume reflection of relativistic protons obtained in [1,2,3]. The features of the scattering of the particles on ring potentials are considered in a wide range of impact parameters.PACS numbers: 61.85.+p, 45.50.Tn In the 1980s, studying the effect of the volume cap-ture of relativistic protons into the channeling regime, Taratin and Vorobiev [4,5] demonstrated the possibility of volume reflection, i.e., the coherent small-angle scattering of particles at angle θ< 2θ L (θ L is the Lindhard critical angle) to the side opposite to the bending of the crystal. Recent experiments reported in [13] confirm the presence of this effect for 1-, 70-, and 400-GeV proton beams in a Si crystal. The conclusions made in [4,5] were based primarily on the numerical simulation. In view of this circumstance, the aim of this work is to derive analytical expressions for the deflection function of relativistic particles. At first sight, the perturbation theory in the potential can be applied at relativistic energies and weak crystal potential [U (r) ≈ 10 − 100]. However, the relativistic generalization of the known classical formula for small-angle scattering in the central field [6],where b is the impact parameter and φ(r) = 2U(r)E p 2 ∞ c 2 , U (r), E, p ∞ are the centrally symmetric continuous potential of bent planes, total energy, and particle momentum at infinity, respectively, is inapplicable for the entire range of impact parameters. Indeed, the above formula is the first nonzero term of the expansion of the classical deflection functionin the power series in the effective interaction potential φ(r). The crystal interaction potential U (r) is the sum of the potentials of individual bent planes concentrically located in the radial direction with period d. It has no singularities (i.e., is bounded in magnitude) and is localized in a narrow ring region at distances R − N d < r < R * JETP Letters, 2008, Vol. 87, No.2, pp. 87 -91 (where the crystal thickness N d << R and N is the number of planes). In this region, U (r) > 0 and U (r) < 0 for the positively and negatively charged scattered particles, respectively. Beyond the ring region, it vanishes rapidly. The perturbation theory in the interaction potential is obviously well applicable if the impact parameter satisfies the inequality b < (R − N d). In this case, the scattering area localized in the potential range is far from the turning point r o determined from the relation b = r o 1 − φ(r o ) and the root singularity of the turning point does not contribute to integral (1). In the general case, it can be shown [7,8] that the condition of the convergence of the power series of φ is a monotonic increase in the function u(r) = r 1 − φ(r) (e.i. u(r) ′ > 0) in the r regions substantial for integral (1). Such a monotonicity is achi...