Knowledge of lithospheric strength can help to understand the internal structure and evolution of the terrestrial planets, as surface topography and gravity fields are controlled mainly by deformational features within the lithosphere. Here, strength profiles of lithosphere were calculated for each planet using a recently updated flow law and taking into account the effect of water on lithospheric deformation. Strength is controlled predominantly by brittle deformation at shallow depths, whereas plastic deformation becomes dominant at greater depths through its sensitivity to temperature. Incorporation of Peierls creep, in which strain rate is exponentially dependent on stress, results in the weakening of plastic strength at higher stress levels, and the transition from brittle to ductile deformation shifts to shallower depths than those calculated using conventional power-law creep. Strength in both the brittle and ductile regimes is highly sensitive to the presence of water, with the overall strength of the lithosphere decreasing markedly under wet conditions. The markedly low frictional coefficient of clay minerals results in a further decrease in brittle strength and is attributed to expansion of the brittle field. As plastic strength is influenced by lithology, a large strength contrast can occur across the crust–mantle boundary if deformation is controlled by ductile deformation. Effective elastic thickness for the terrestrial planets calculated from the rheological models indicates its close dependence on spatiotemporal variations in temperature and the presence of water. Although application of the strength models to observed large-scale surface deformational features is subject to large extrapolation and uncertainties, I emphasize the different sensitivity of these features to temperature and water, meaning that quantifying these features (e.g., by data from orbiting satellites or rovers) should help to constrain the internal structure and evolution of the terrestrial planets.