In the last decade, preoperative modelling of the treatment of cerebral aneurysms is being actively developed. Fluid-structure interaction problem is a key point of a such modelling. Hence arises the question about the reasonable choice of the model of the vessel and aneurysm wall material to build the adequate model from the physical point of view. This study covers experimental investigation of 8 tissue samples of cerebral aneurysms and 1 tissue sample of a healthy cerebral artery. Results on statistical significance in ultimate stress for the classification of 2 cohorts of aneurysms: ruptured and unruptured described earlier in the literature were confirmed (p ≤ 0.01). We used the four most common models of hyperelastic material: Yeoh, Neo-Hookean and Mooney-Rivlin (3 and 5 parameter) models to describe the experimental data. In this study for the first time, we obtained a classification of hyperelastic models of cerebral aneurysm tissue, which allows to choose the most appropriate model for the simulation problems requirements depending on the physical interpretation of the considered problem: aneurysm status and range of deformation.