The bachelor's thesis deals with possibilities of analytical solution of stress-strain states of arteries. The first part of the thesis gives an information about cardiovascular system and continuum mechanics. The calculation was performed analytically and also numerically using ANSYS program. The analytical calculation was carried out considering non-linear theory of thin and thick-walled vessels involving the residual stress and fictitious temperature approach. Furthermore, the analysis of solutions of abdominal aortic aneurysms was done based on linear theory. Description of other methods of linear theory and techniques of calculating with residual stress are briefly summarized