This paper presents an analysis of hyperelastic constitutive models for continuous bodies both from a modeling and numerical point of view. Contributions are made within the context of finite element numerical simulations. Numerical results with relevance to flows in the cardiovascular system are outlined in the case of a sophisticated fluid–structure interaction problem, in specific complex geometries of anatomically accurate cerebral arteries in diseased state. In this regard, the work carefully outlines the numerical validation of constitutive models for healthy and unhealthy cerebral arterial tissues by means of simulations of static inflation tests on an idealized specimen of anterior cerebral artery (ACA). The healthy tissue is described by means of isotropic and anisotropic models that, are fitted with respect to experimental data describing the mechanical behavior of the ACA; the numerical results are presented highlighting the most important numerical aspects influencing the correct and efficient simulation of the mechanics of continuous bodies such as, for instance, the arterial wall. We further consider numerical simulations of unhealthy conditions of the tissue by taking into account different levels of weakening of its mechanical properties. Taking the cerebral cardiovascular system as a challenging test problem, we focus on the study of the effects of the imposed mechanical levels of degradation on kinematic quantities of interest by simulating static inflation tests for the different models. This work does not aim to propose a new mathematical model for the mechanical damage occurring at the onset of cardiovascular diseases such as cerebral aneurysms. The modeling and numerical techniques presented may be applied to a wide range of problems, equally challenging to that of the cardiovascular system with complex structural models and fluid-structure coupling.