Magnetic configurations of finite-length chains of Mn atoms on a Pt(332) surface have been theoretically studied within a classical model taking into account the exchange Heisenberg interaction, biaxial magnetocrystalline anisotropy, the Dzyaloshinskii–Moriya interaction, the dipole–dipole interaction, and the Zeeman interaction of the magnetic moments of atoms with an external magnetic field. It has been shown that both nearly collinear and helical magnetic states can be stable. An applied magnetic field causes the rotation of the plane in which the helical magnetic structure lies. The stability of these states in the external magnetic field parallel to the easy axis has been examined. It has been found that the Mn/Pt(332) system is characterized by two critical fields, the lower of which is associated with the finite length of the atomic chain. The predicted effects are due to the Dzyaloshinskii–Moriya interaction and can be observed experimentally.