Increased arterial stiffness, i.e. reduced arterial elasticity and compliance, is closely linked to aging and cardiovascular diseases. It is an important predictor of cardiovascular risk and indicator of the stage of a cardiovascular disease. This means arterial stiffness evaluation is crucial for early detection of diseases, disease monitoring, and treatment management. Thus, numerous non-invasive techniques, such as pulse wave velocity, ultrasound-based methods, and arterial pressure waveform analysis, have been developed. However, it is very well known that mechanical behaviour of arterial tissue is highly nonlinear, meaning that it is impossible to describe arterial wall stiffness with a single stiffness parameter. Therefore, despite significant progress, challenges remain, and numerous studies are still being conducted trying to accurately estimate arterial stiffness and associated health risks. Furthermore, one of the key characteristics of the arterial wall is presence of residual stresses in unloaded configuration, a consequence of different deformations of constituents within the wall, which is often neglected in parameter estimations. In this work, an improved approach for estimation of material properties of arteries through non-invasively measured pressure and diameter data is presented. The method is first applied on virtual experiments from finite elements, but also on invasive or ex vivo test data (inflation–extension and biaxial tests performed on the same vessel). The difference in homeostatic stresses calculated with standard and improved methods will be shown. ACKNOWLEDGMENT This paper has been funded by the European Union (NextGenerationEU) under the National Recovery and Resilience Plan 2021–2026 (NRRP), through the UNIZAG FSB institutional project “Determining the geometry of personalized medical implants”, approved by the Ministry of Science, Education and Youth of the Republic of Croatia (component C3.2, source 581). The author also thanks Gerhard Sommer (TU Graz) for experimental data.