The objective of this study was to determine the orientation and magnitude of maximal displacement forces (DFs) in the thoracic aortic aneurysm endograft (TAA endograft) in three-dimensional (3D) space. Theoretical computer model representing the anatomically worst-case scenario with respect to DF magnitude was used to calculate the magnitude and orientation of maximal DF. A patient-specific anatomical computer model of typically seen, average size anatomy was used to analyse the progression of DF throughout the cardiac cycle. Maximal DFs were 35.01 and 37.32 N in standing and supine position, respectively, in 46-mm diameter TAA graft with 90° bend. A patient-specific model shows that a maximal DF magnitude is achieved at the peak systolic flow. In both models, the orientation of the DF vector was perpendicular to the greater curvature of the aorta, with upward (cranial) and sideways components. The effect of shearing force on the total DF that acts on the TAA endograft was found negligible due to the several orders of magnitude stronger contribution of pressure forces to the total DF relative to the wall shear stress contribution, resulting in aortic diameters and angulation being the main drivers of DF. It was discovered that the TAA endografts can be subjected to much stronger DF than previously suspected. The magnitude of maximal DF in thoracic aorta in the worst-case scenario could be as high as 35.01 N (standing) and 37.32 N (supine). This new information should be used in the process of designing new generations of TAA endografts with better migration resistance properties.