Objective: To investigate the degree of stenosis of the internal carotid artery required for continuous blood flow in an interposition vein bypass to the middle cerebral artery. Methods: Computational fluid dynamics techniques were used to investigate a case of common carotid to middle cerebral artery brain bypass with varying degrees of internal carotid artery stenosis. Blood flow patterns across the patient-specific brain bypass were evaluated. Results: Simulation found that for cross section stenosis of less than 60%, no flow occurred in the bypass graft. Further narrowing of the internal carotid artery increased flow linearly within the bypass graft. There was significant energy loss and pressure gradient difference between the proximal and distal anastomosis sites of the bypass. Conclusion: Computational fluid dynamics helps us to quantify the flow distribution, wall shear stress and pressure gradient in brain bypass surgery. The angle of the distal anastomosis had no effect on hemodynamic indices, allowing this consideration to be ignored in modeling. This modeling technique is useful to estimate the required degree of stenosis in the artery that is to be occluded to ensure sustained flow in the bypass. This will be of importance where there is staged surgery with a time interval between the bypass and the definitive internal carotid artery occlusion.