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Brain aneurysms are pathological dilatations of cerebral arteries and are known as one of the most common and serious cerebrovascular events. However, patients with cerebral aneurysms do not exhibit evident symptoms until they rupture. The main objective of the present study is to perform numerical characterizations of the biomechanical behavior of aneurysms in order to analyze the blood vessel wall behavior during the formation of an aneurysm. By taking into account different geometric and physiological parameters, flow simulations of a well-known Newtonian fluid (glycerin) was performed using the commercial finite volume method package Ansys® - Fluent, and pressure along the channel was determined. These pressures were imported into the channel, in the Ansys®- Static Structural, in order to evaluate and analyze the displacement and strain fields in the channel wall, caused by the internal pressure induced by the fluid flow. All calculations were performed by using the most widely accepted hyperelastic constitutive models and it was found that any constitutive model can be applied to this kind of studies, allowing to visualize where pressure achieves its maximum value and consequently, the most favorable region where the rupture is more likely to occur.