Hypertension results in a thickening of the arterial wall due to a net increase in wall constituents via a coordinated production and removal of smooth muscle and extracellular matrix. Although many reports address the associated changes in material properties, few models address the biomechanics of the growth and remodeling process. In this paper, we employ a new, fundamentally different approach to modeling arterial adaptation in hypertension. In particular, basic, characteristic features of hypertension are simulated using a constrained mixture model wherein individual constituents can turnover at different rates and can have different natural configurations. We show, for example, that if there is no turnover of elastin (which approximates responses in maturity), the model vessel is able to reduce an early elevation in wall stress via a thickening of the wall even though the adaptation may be suboptimal. Conversely, if all constituents can turnover completely (which may approximate late development), the model vessel can restore the state of stress and material properties to native values. Given the potential of such a model, there is a need for more data on the history of turnover of individual constituents and their individual material properties.