Multiphase flows with gas holdup are found in numerous process engineering applications. A targeted flow and process optimization of the plant technology requires a profound un derstanding of the process. A vital characteristic of these processes is the spatially resolved gas holdup, which describes the local ratio of the bubble volume to the total volume under consideration. Determining the gas holdup is the subject of current research due to its relevance for the process understanding in process engineering. Besides the enhanced understanding of the process, the determined gas holdup distribution can be utilized as a basis for optimizing the plant technology or monitoring the process during operation. However, due to the limitations of existing methods, a detailed measurement of entire plants can only be realized to a limited extent in practice. The concept of gas holdup estimation via acoustic transmission tomography (GATT) offers an alternative, non-invasive approach to the existing measurement techniques. The concept utilizes the dependence of the speed of sound on the gas holdup (isothermal Wood correlation). In this thesis, based on this concept, a novel acoustic method for tomographic determination of gas holdup distribution is developed, investigated, and discussed. The proposed method provides a promising approach, which is already capable of reconstructing spatially resolved gas holdup distributions with sufficient accuracy. This results in a broad potential field of application for this method in research and development as well as process monitoring in the fields of process engineering.