Ceres, the largest body in the asteroid belt (940 km diameter), provides a unique opportunity to study the interior structure of a volatile-rich dwarf planet. Variations in a planetary body's subsurface rheology and density affect the rate of topographic relaxation. Preferential attenuation of long wavelength topography (≥150 km) on Ceres suggests that the viscosity of its crust decreases with increasing depth. We present finite element (FE) geodynamical simulations of Ceres to identify the internal structures and compositions that best reproduce its topography as observed by the NASA Dawn mission. We infer that Ceres has a mechanically strong crust with maximum effective viscosity ∼1025 Pa s. Combined with density constraints, this rheology suggests a crustal composition of carbonates or phyllosilicates, water ice, and at least 30 volume percent (vol.%) low-density, high-strength phases most consistent with salt and/or clathrate hydrates. The inference of these crustal materials supports the past existence of a global ocean, consistent with the observed surface composition. Meanwhile, we infer that the uppermost ≥60 km of the silicate-rich mantle is mechanically weak with viscosity <1021 Pa s, suggesting the presence of liquid pore fluids in this region and a low temperature history that avoided igneous differentiation due to late accretion or efficient heat loss through hydrothermal processes.