The cardiovascular system is characterized by complex interactions between various control mechanisms and physiological processes. Different approaches are used to provide better diagnostics and physiological understanding, cardiac prosthesis and medical planning. The mathematical description and modelling of the human cardiovascular system plays nowadays an important role in the comprehension of the genesis and development of cardiovascular disorders by providing computer based simulation of dynamic processes in this system. This paper aims to give an overview on lumped parameter models that have been developed by many researchers all over the world, to simulate the blood flow in systemic arteries. Surveying various references we make a review of different approaches to arterial tree modelling and discuss on the applications of such models.