The present thesis is a report of investigations on a model for computing the water flow in the wave tank of the OSU Wave Laboratory. A wave board, established at one end of the 100 m long, 4 m wide and 6 m deep wave tank, produces water waves by periodically moving back and forth. The resulting free surface water flow will be modeled physically. This physical model will be transformed into a mathematical model which is implemented on a computer. The goal is to approximately compute the velocity distribution of the fluid modeled as a linear combination of basis functions. Certain well known mathematical tools such as the Galerkin method or the idea of finite elements are employed. The theoretical developments are done for the three-dimensional case. However, numerical experiments are performed in two dimensions only. Two different types of basis functions will be introduced and investigated. Their advantages, disadvantages and capability to compute realistic results will clearly be shown and demonstrated in practice. Several problems occured during the development of the computation algorithms. These problems are outlined in this thesis, and several solutions are suggested. For example, a method how to deal with rising and falling water surface at a vertical boundary will be presented. The results of five numerical test runs will be exhibited, underlining what the theory predicts.