This study aims to investigate the haemodynamic response induced by implantation of a double-branched endograft used in thoracic endovascular aortic repair (TEVAR) of the aortic arch. Anatomically realistic models were reconstructed from CT images obtained from patients who underwent TEVAR using the RelayPlus double-branched endograft implanted in the aortic arch. Two cases (Patient 1, Patient 2) were included here, both patients presented with type A aortic dissection before TEVAR. To examine the influence of inner tunnel branch diameters on localised flow patterns, three tunnel branch diameters were tested using the geometric model reconstructed for Patient 1. Pulsatile blood flow through the models was simulated by numerically solving the Navier–Stokes equations along with a transitional flow model. The physiological boundary conditions were imposed at the model inlet and outlets, while the wall was assumed to be rigid. Our simulation results showed that the double-branched endograft allowed for the sufficient perfusion of blood to the supra-aortic branches and restored flow patterns expected in normal aortas. The diameter of tunnel branches in the device plays a crucial role in the development of flow downstream of the branches and thus must be selected carefully based on the overall geometry of the vessel. Given the importance of wall shear stress in vascular remodelling and thrombus formation, longitudinal studies should be performed in the future in order to elucidate the role of tunnel branch diameters in long-term patency of the supra-aortic branches following TEVAR with the double-branched endograft.