This paper is closely related to one of the worlds most common cardiovascular diseases by the name intracranial aneurysm, which referes to a localized dilation or ballooning of the blood vessel in the brain. Aneurysms have a high risk of rupture. If an aneurysm ruptures, blood leaks into the space around the brain, which can lead to sudden death. In order to better understand the causes and consequences of cardiovascular diseases, there is a need for carrying out mechanical tests in order to determine reliable material properties of cardiovascular tissues. The subject matter of this paper is divided into two parts. In the first part, experimental testings are being conducted for a range of selected different polymer materials, with which strain–stiffening behavior of soft tissues (i.e. arteries) wants to be mimicked. The specimens, that were fabricated by the means of 3D printing technique called PolyJet, are subjected to a uniaxial tensile test. From the experimental data employing optimization fitting procedure, material parameters of different hyperelastic constitutive models are determined. Hyperelastic material models are used in continuum mechanics approaches for describing the typical behaviour of polymer materials. In the second part, implementation of selected hyperelastic material models into a finite element software Abaqus is being done throughout a user–defined subroutine called UMAT. In order to accomplish a successful implementation, development of Fortran 77 code is needed. Following a defined set of rules for this kind of material constitutive model implementation, the code should contain all the variables for a particular hyperelastic model which are necessary to run a nonlinear incremental and iterative finite element method analysis in Abaqus.