jats:titleAbstract</jats:title>jats:pWe employ laboratory‐based grain size‐ and temperature‐sensitive rheological models to describe the viscoelastic behavior and tidal response of terrestrial bodies with focus on Mars. We consider five rheological models: Maxwell, extended Burgers, Andrade, Sundberg‐Cooper, and a power law approximation. The question of which model provides the most appropriate description of dissipation in planetary bodies, remains an open issue. To examine this, we build crust and mantle models of Mars (density and elasticity) that are computed self‐consistently through phase equilibrium calculations as a function of pressure, temperature, and bulk composition, whereas core properties are based on an Fe‐S parameterization. We assess the compatibility of the viscoelastic models by inverting tidal response, mean density, and moment of inertia of Mars for its thermal, elastic, and attenuation structure. Our results show that although all viscoelastic models fit the data, (1) their predictions of the tidal response at other periods and harmonic degrees are distinct, implying that our approach can be used to distinguish between the various models from seismic and/or tidal observations (e.g., with InSight), and (2) Maxwell is only capable of fitting data for unrealistically low viscosities. All viscoelastic models converge upon similar interior structure models: large liquid cores (1,750–1,890 km in radius) that contain 17–20.5 wt% S and, consequently, no silicate perovskite‐dominated lower mantle. Finally, the methodology proposed here is generally formulated and applicable to other solar and extrasolar system bodies where the study of tidal dissipation presents an important means for determining interior structure.</jats:p>