The duration of arteriovenous anastomoses functioning is influenced by haemodynamic conditions and the properties of the formed vascular access, which determine the mechanisms of vascular wall restructuring, neointima formation, lumen remodelling, and stenosis development. The aim of the study: mathematical justification of the haemodynamic and structural features of different types of arteriovenous anastomoses. Arteriovenous anastomoses between the common carotid artery and the external jugular vein of two types were formed in rabbits: end-to-side (1st group) and end-to-side with the use of venous tributaries (2nd group). It has been confirmed that variations in the geometry of the anastomosis affect the amount of blood circulation by altering its diameter. The peculiarities of local blood flow directly determine the restructuring of the endothelium and smooth muscle cells. The calculated blood flow velocity in the arterial and venous parts of the anastomoses corresponds to the values established by ultrasound examination within two hours after the formation of vascular access. The obtained data reflect haemodynamic parameters in the early period after fistula formation, before blood flow is enhanced by vasodilation and a decrease in peripheral vascular resistance. Such a level of haemodynamic load is sufficient to trigger a cascade of adaptive remodelling of the venous wall and its transition to an arterial phenotype, without creating excessive mechanical stress associated with the risk of intimal hyperplasia. The established data of haemodynamic indexes confirm the physiological validity of the developed models and provide a basis for further comparison of the calculated indicators with actual ultrasound values and morphological features of vascular access at different stages of fistula maturation. The proposed analytical interpretation is consistent with established haemodynamic indexes, as well as the structural organisation of vessels and ultrastructural changes in the endothelium of the formed anastomosis. The developed mathematical model enables the prediction of vascular access haemodynamics features, the selection and justification of a specific connection type, and the assessment of structural damage risks and the probability of their development.