Objective. Low-intensity transcranial ultrasound stimulation (TUS) is a promising non-invasive brain stimulation (NIBS) technique. TUS can reach deeper areas and target smaller regions in the brain than other NIBS techniques, but its application in humans is hampered by the lack of a straightforward and reliable procedure to predict the induced ultrasound exposure. Here, we examined how skull modeling affects computer simulations of TUS. Approach. We characterized the ultrasonic beam after transmission through a sheep skull with a hydrophone and performed computed tomography (CT) image-based simulations of the experimental setup. To study the skull model s impact, we varied: CT acquisition parameters (tube voltage, dose, filter sharpness), image interpolation, segmentation parameters, acoustic property maps (speed-of-sound, density, attenuation), and transducer-position mismatches. We compared the impact of modeling parameter changes on model predictions and on measurement agreement. Spatial-peak intensity and location, total power, and the Gamma metric (a measure for distribution differences) were used as quantitative criteria. Modeling-based sensitivity analysis was also performed for two human head models. Main results. Sheep skull attenuation assignment and transducer positioning had the most important impact on spatial peak intensity (overestimation up to 300%, respectively 30%), followed by filter sharpness and tube voltage (up to 20%), requiring calibration of the mapping functions. Positioning and skull-heterogeneity-structure strongly affected the intensity distribution (gamma tolerances exceeded in >80%, respectively >150%, of the focus-volume in water), necessitating image-based personalized modeling. Simulation results in human models consistently demonstrate a high sensitivity to the skull-heterogeneity model, attenuation tuning, and transducer shifts, the magnitude of which depends on the underlying skull structure complexity. Significance. Our study reveals the importance of properly modeling the skull-heterogeneity and its structure and of accurately reproducing the transducer position. The results raise red flags when translating modeling approaches among clinical sites without proper standardization and/or recalibration of the imaging and modeling parameters.