In this doctoral thesis the numerical simulation of stirred suspensions is investigated using the Euler-Lagrange approach. For this purpose it was necessary to develop a 3d code on the basis of an existing 2d code. The special requirements of flow calculations in stirred tanks had to be taken into account. In achieving a fundamental understanding of two-phase flows it is essential to deepen in their theoretical background. In particular, the equations of conservation, turbulence modeling, particle dispersion, two- and four-way coupling are discussed in detail. Equally important is the treatment of the impeller action towards the numerical implementation. Furthermore, error estimations and speed-up possibilities are dealt with. The successful validation of the modeling is accomplished through various test cases. Because of the importance of particle-particle collisions for the considered calculations, the two-phase vertical pipe flow case is chosen for representation. Finally, the flow in a baffled stirred vessel equipped with a pitched-blade turbine is investigated numerically and experimentally, considering a two-phase system consisting of water and glass beads. The comparison of simulations with gathered measurements showed good overall agreement of the fluid and particle velocities. For the calculations, up to 2 million control volumes (hexahedrons) are used on a half-model. The dimensionless distance from the wall is analyzed in combination with the logarthmic wall function to prevent significant errors in calculating the pumping capacity of the impeller. The examination of the convective flux discretisation and the grid resolution reveals the significant role of the weighting factor γCDS in the calculation of reliable flow structures. The grid size mainly affects the turbulent quantities. Normed values of the calculated as well as measured velocities show an excellent correlation with the impeller speed. The number of calculated particle trajectories is to be defined on the basis of a justifiable compromise between accuracy and calculation time. One of the most important indicators for stirred suspensions is the power number, whose calculation agrees very well with literature data. From the different criteria to estimate coupling convergence, the monitoring of the power number proves to be the best choice. The introduction of inner Lagrange-loops does not accelerate convergence in a significant manner because of de-coupling effects. In general, the particles follow the fluid flow very well. Significant slip velocities only occur in the impeller region and near the wall. The impeller stream gets broader due to dispersion of the particles. It is important to realize that parameter variations (grid resolution, particle size, mean particle volume fraction) have a larger influence on the threedimensional distribution of the particles than on the respective velocities. The local Stokes number is estimated to evaluate the importance of particle-particle collisions, where larger Stokes numbers imply that collisions are more likely. Through this it is shown that relevant collisions occur only in a few delimited areas. Nevertheless, calculations show a large effect of phase coupling and particle-particle collisions even at relatively low mean particle volume fractions. The particle distribution tends to get more homogeneous as a result of collisions. As a matter of fact, high local concentrations, e.g. at the bottom of the vessel, are drastically reduced. Non-physical local concentration peaks are amplified with increased grid resolution and therefore the consideration of particle-particle collisions becomes even more relevant.