Lithospheric density and thickness variations are important contributors to the state of stress of the plates. The relationship between the lithosphere's isostatic state, subcrustal structure and stress field, however, remains unresolved due to the uncertainties on its thickness, composition and rheology. To study the influence of lithospheric structure on intraplate stresses, we use a new model of global lithospheric structure (TDL) that accounts for the presence of depleted mantle to explore the effects of isostatic compensation, mantle density structure, lithospheric thickness (base depth) and mechanical coupling within the lithosphere on wavelengths >200 km. We compute the mean lithostatic stress (Ω) of 2°× 2° lithospheric columns and then solve for the resulting global ‘tectonic’ stress field for a homogeneous elastic lithosphere with the finite element package ABAQUS. For a 100 km base depth, a historically common value for lithospheric thickness, tectonic stress patterns are largely insensitive to mantle density structure and match patterns in the world stress map, for both isostatically compensanted and non-compensated lithospheric structure. Increasing the base depth up to 250 km to account for thick continental roots, however, leads to sharp variations in the stress field between isostatic lithospheric structure models and TDL as the mantle portion of the lithosphere dominates Ω. Decreasing the model base depths up to 25 km as a proxy for vertical strength variations due to low viscosity channels within the crust or lithosphere as a whole, strongly alters stresses in magnitude, azimuth and regime, as the influence of topography and shallow crustal structure increases. We find that restricting spatial changes in Ω to a specified region to mimic lateral variations in strength also has a large effect on the resulting stresses, which leads us to conclude that regional models may not always be adequate for modelling the stress field. Strong deviations from long-wavelength patterns on the world stress map in models with a shallow (<<100 km) or deep (>>150 km) uncompensated model base depth likely reflect that the globally averaged lithospheric thickness is close to 100 km and large deviations from this depth generate unrealistic stress patterns related to uncompensated buoyancy forces. Because the stresses are so sensitive to base depth, we conclude that using Ω to represent spatial and vertical variations in lithospheric structure is not an adequate approximation. Our results suggest that future studies must incorporate the full 3-D variations in density and rheology of the lithosphere to elucidate the source and nature of the lithospheric stress field. These studies have become possible with the advent of modern computational tools and advances in our knowledge of lithospheric structure and rheology.