Cardiovascular diseases are the most common causes of death in the modern society. To improve the diagnosis and further the therapy of such diseases, dynamic models for the heart circulation system are used more and more often. In these models, the main factors which must be considered are accurateness, computing time and identifiability of the parameters. Therefore, one dimensional models, which have in fact a high efficiency, come to the center of attention. The aim of this master thesis is to simulate the bloodstream through networks of blood vessels with the Finite Element Method in one dimension. The starting points are the general Navier-Stokes equations which build the basis for fluid mechanics. Based on these very complex equations a one dimensional model is derived using additional assumptions. In this context, it is not only very important to understand the biological behavior of human blood vessels, but also to have a profound knowledge about blood pressure, wave propagation and other factors which will have an influence on the simulation. The precedent model condition is that an artery can be represented by an axisymmetric cylinder in which certain flow and pressure conditions exist. As result a one dimensional system of partial differential equations is derived. This system can be written in hyperbolic conservation form with the state variables crosssectional area, the flow, the velocity and the pressure. To solve the system of partial differential equations, numerically correct boundary conditions have to be considered. To be more precise, the main questions are on the one hand, how to simulate the input from the heart, and on the other hand, how to simulate the load downstream and compliance in a physiological way. For the input, a pressure function is used. To simulate the load downstream and the compliance of the arteries, a Windkessel model consisting of three elements is used. The literature has shown that this model can simulate the physiological effects which appear in a system of arteries in a realistic way. Furthermore, a main part of this thesis is to describe bifurcations, the branching of the arteries. By using bifurcations the considered abstract vascular networks can be simulated. In this context two conditions have to be fulfilled. Firstly, same pressure in all branches and, secondly, mass conservation at the junction. With these two conditions, a nonlinear system of equations is set up and solved to simulate bifurcations. The partial differential equation system cannot be solved analytically. Hence, to solve it in this thesis a numerical Finite Element Method is used. To set up a Finite Element Method a discretization in space and time has to be done. In this context, a Taylor Galerkin method of second order with basic functions of first order is used. With this method, efficiency and stability limitations are reached and therefore a second method, the Discontinuous Galerkin method with high order Legendre polynomial as basic functions is considered. The model is implemented by using the mathematical software Matlab. To verify the model, several simulations are done, using one artery, one bifurcation consisting of three arteries and an abstract arterial tree built up by thirteen central arteries. In all simulations, the parameters of the Windkessel model and the parameters of the arteries are based on experiments and on physiological values. In all tests, physiologically realistic results are obtained. After that, the calculations are verified with published results of already accomplished models. The comparison shows very good agreements. Furthermore, the two numerical methods, namely the Taylor-Galerkin and the Discontinuous Galerkin method, are compared by the simulation of one arterial segment. The same results are obtained with both methods. However, it can be seen that the Discontinuous Galerkin method has a higher computational efficiency than the Taylor-Galerkin method. It can be concluded that the application of a one dimensional Finite Element Method approach along with the particular implementation presented can describe the effects in a system of human arteries in a realistic way and, on top of that, has a shorter computing time. A field of application for this model is the early diagnosis of cardiovascular diseases. With measurements gained from healthy patients, the model can be parameterized. The calculations from this model can be compared with measurements from patients with cardiovascular diseases in order to conclude about abnormal changes in the cardiovascular system.