Abstract The diagnostic possibilities of the free oscillation method for probing the global pattern of the structure of the Mars interior (the radius and aggregate (solid or liquid) state of the core, the crust thickness, the depth of the beginning of the olivine-spinel phase transition, and the width of this transition) are investigated. A set of two-layer models for different compositions of the FeFeS system are used to investigate the aggregate state of the core and its radius. The effects of the crust thickness and the depth of the beginning of the olivine-spinel phase transition are investigated for four- and five-layer models. The high-(HTM) and low-(LTM) temperature models are considered. For a large number of models spheroidal oscillations are calculated for n= 2–200. Dispersion curves are constructed for Rayleigh waves, providing a valuable tool for diagnosing the core thickness. The oscillation periods with low values n⩽7 depend substantially on the core parameters, while the spheroidal modes with n ≈ 7–10 diagnose reliably the position and structure of the transition zone.