Shadows add a level of realism to a rendered image. Furthermore, they support the user of an augmented reality application through the interactions of virtual objects. The reason for this is that shadows make it easier to judge the position and the size of a virtual object. In 1978, Lance Williams published the shadow mapping algorithm with the aim to render a shadow of objects in a virtual scene. This master thesis presents a modified shadow mapping approach that can additionally be used in Augmented/Mixed Reality applications. First of all the standard algorithm ist extended by a PCF-filter. This filter is used to handle the aliasing-problem on the edges of the shadow and also to soften the shadow. Phantom objects are necessary to be able to operate this approach in a Mixed Reality application. These objects simulate the position and the geometry of the real objects for the algorithm. The approach consists of three steps: First the camera image is drawn into the framebuffer. After that a shadow map, of the virtual objects only, is created. When rendering these objects shadow mapping creates the shadows of virtual objects onto other virtual objects and on themselves. Afterwards the phantom objects are rendered. The depth test is performed on the fragment shader. If a fragment lies in a shadowed region it will get the color of the shadow. However, if it is beeing lit its transpareny value will be set to 1 so that it will not be seen. By applying this procedure all shadows from the virtual objects onto the real objects will be drawn. The results show that the approach can be used in real time in Mixed Reality environments. Additionally a comparison with a modified version of a shadow volume algorithm that can also be used for Mixed Reality applications shows that the approach of this master thesis casts a more realistic shadow in a shorter period of time. All in all this approach increases the level of realism in augmented reality applications and it helps the user measure distances and sizes of the virtual objects more easily.