Endovascular aortic stent-graft is a new, minimally invasive procedure for treating thoracic aortic diseases, and has quickly evolved to be one of the standard treatments subject to anatomic constraints. Stent-graft deployment in the thoracic aorta, especially close to the aortic arch, normally experiences a significant drag force which might lead to the risk of stent-graft failure. A comprehensive investigation on the biomechanical factors affecting the drag force on a stent-graft in the thoracic aorta is thus in order, and the goal here is to perform an in-depth study on the contributing biomechanical factors. Three factors affecting the deployed stent-graft are considered, namely, the internal diameter of the vessel, the starting position of the graft and the diameter of curvature of the aortic arch. Computational fluid dynamic techniques are applied to model the blood flow. The three-dimensional continuity equation and the time-dependent Navier-Stokes equations for an incompressible fluid were solved numerically. The drag force due to the change of momentum within the stent-graft and the shear stress were calculated and analyzed. The drag force on a stent-graft will depend critically on the internal diameter and the starting position of stent-graft deployment. Larger internal diameter leads to larger drag force and the stent-graft deployed at the more distal position may be associated with significantly diminished drag force. Smaller diameter of curvature of the aortic arch results in a decrease of the drag force. These findings may have important implications for the choice and design of stent-grafts in the future.