The submonolayer adsorption of Na onto the Cu(110) surface is studied. At small Na coverages (Θ = 0.16–0.25 ML), the substrate surface subjected to missing-row reconstruction (1 × 2) is shown to be most stable dynamically. When the coverage increases to Θ = 0.5 ML, the unreconstructed substrate surface with a c(2 × 2) sodium adlayer becomes dynamically stable. For an analysis, we used data on the equilibrium atomic configuration, the adsorption energy, the phonon spectra, the local density of phonon states, and the polarization of localized vibrational modes. All calculations were performed using the interatomic potentials obtained in terms of the embedded-atom method. The calculated frequencies of localized vibrational modes agree well with the existing experimental data.