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The growth of one and two atomic layers of iron on a W(110) substrate was followed by low-energy electron microscopy. The near-surface structural properties of the perfectly flat pseudomorphic films were studied by quantitative low-energy electron diffraction analysis from areas of uniform thickness as well as by the density functional theory. A strong relaxation of the outermost atomic layers was found in Fe mono- and bilayers on W(110). By calculating the phonon dispersion relations and phonon density of states, the stability of the pseudomorphic iron bilayer on a tungsten substrate has been addressed. To complete the physical picture, an iron trilayer has also been analyzed in order to identify the source of instability for its pseudomorphic phase. Our results show that the surface instability originates from the softening of the in-plane surface modes along the [110] direction, although the soft modes were not observed. The enhanced magnetic moments calculated within the density functional theory are in good agreement with experimental findings reported for these systems.