The purpose of this thesis is to develop a non-linear, one-dimensional (1-D) model of pulse wave propagation in arterial networks in the cardiovacular system. Arteries are stimulated as thin, homogeneous and elastic tubes and the blood as a homogeneous, incompressible, and Newtonian fluid. The governing equations are analysed by means of the method of characteristics and are solved using a discontinuous Galerkin scheme, with a 1-D spectral/hp element spatial discretisation and a second-order Adams-Bashforth time-integration scheme. A linearised model is also studied to obtain analytical solutions that are very useful in providing insight into the interpretation of the results. The modelling capabilities of the existing 1-D code are enhanced by including viscous dissipation and more realistic models of the inflow and outlfow boundary conditions. The new code is validated against a well-defined experimental model and against in-vivo data when available. It is applied to study pulse propagation along the humann aorta to understand the pulse waveforms measured in-vivo, and to study the effect of anastomoses in two arterial networks: the arm and cerebral circulation. In the arm, the reliability of the modified Allen's test to determine the presence of sufficient collateral flow through the palmar arch artery is assessed. In the cerebral circulation, the ability of the circle of Willis to compensate for partial or total occlusions of arteries is examined. The main contribution of this thesis has been the development and validation of a relaible 1-D model that produces clinically relevant results with a reasonable computational cost. This model offers an important insight into the performance of the arterial system, in healthy conditions and after total or partial occlusions of arteries, and it has the potential to assist in the diagnosis and treatment of cardiovascular diseases if applied with patient-specific data.