Cardiovascular disease has caused 3.9 million deaths in Europe and over 1.8 million deaths in the European Union, which accounts for 45\% of all deaths in Europe and 37\% of all death in the European Union in 2017. Cardiovascular disease is mainly caused by atherosclerosis. Atherosclerosis is a kind of disease where the inside of the artery gets narrow due to the build-up of plaque. Plaque is an abnormal accumulation of material in the inner layer of the arterial wall. A swelling can be formed by the accumulated material. The swelling may intrude into the channel of the artery wall, which will make the channel get narrower and restrict blood flow. Based on current medical technology, images of the plaques can be taken. However, there are no efficient simulation tools for plaque rupture. In order to set up sufficient simulation tools, a good representation of the material behaviour and the progression of the failure is needed. There are material models for the arterial wall accounting for large deformations (hyperelasticity) and anisotropy in the material response. And, there are also failure models. However, the material models and the failure models have not been combined. In this thesis, three material models and one failure model are included. The three material models are Neo-Hookean material model and two anisotropic models developed for arterial wall tissue developed by Holzapfel and Gasser. They are combined with anisotropic damage model to obtain three new constitutive models for failure of hyperelastic material. After the three constitutive models are set up, a parameter study is performed to explore the material properties of the new constitutive models. Verification of the material models is also included. Finally, the performance of the model is demonstrated with failure analyses on different geometries: a simple plane, a bar, a plane with an imperfection and a plane with a rectangular hole in the middle.