Arteriopathy in Williams-Beuren syndrome (WBS) patients with elastin gene deletion represents the most important mortality and mobidity causes and seems directly correlated with elastin quantity. There is a need for a comprehensive model that accounts for the quantity of elastin and its role in the geometry and biomechanical properties of artery. Such model might improve our understanding of the pathophysiology and improve innovation in drug development for WBS. We present an in silico model for the adaptation of human carotid artery in response to elastin deficiency. The model is based on the hypothesis that elastin deficiency-induced growth and remodelling occurs via the excessive production of vascular smooth muscle cells (VSMCs), change in collagen engagement, and increased laminar units to ensure that the average stress of lamina unit in the homeostatic state is unchanged under normal condition. Using an elastin-stress driven model and a constituents-based model, which considers the contributions of elastin, collagen, and VSMCs in an explicit form, we illustrate capabilities of the model in predicting the arterial thickness and biomechanical properties with varying elastin quantity before and after elastin restoration. Alternatively, the model has the potential to estimate, indirectly, the fraction of remaining elastin using the values of arterial thickness and mechanical properties. Our model provides a new approach for mathematically assessing the arterial growth and remodelling in human vascular disease with insight into the importance of constituent distributions.