The brain is supplied by the internal carotid and vertebro-basilar systems of vessels interconnected by arterial anastomoses and forming at the base of the brain a structure called the Circle of Willis (CoW). An active intrinsic ability of cerebral vascular bed maintains constant Cerebral Blood Flow (CBF) in a certain range of systemic pressure changes. This ability is called autoregulation and together with the redundant structure of the CoW guarantee maintaining CBF even in partial occlusion of supplying arteries. However, there are some situations when the combination of those two mechanisms causes an opposite effect called the Reversed Robin Hood Syndrome (RRHS). In this work we proposed a model of the CoW with autoregulation mechanism and investigated a RRHS which may occur in the case of Internal Carotid Artery (ICA) stenosis combined with hypercapnia. We showed and analyzed the mechanism of stealing the blood by the contralateral side of the brain. Our results were qualitatively compared with the clinical reports available in the literature.