Regarding to the growth of the use of the amount of Hydrofoils and Airfoils in many industries, the necessity of developing most efficient types of these foils is becoming more obvious and thus many different methods related to this subject have been examined. Since their performance is straightly related to the lift force due to the flow over the hydrofoils, the biggest endeavor to increase the efficiency is concentrated on the increase of this force. One approach to achieve this goal is to prepare certain boundary conditions for the foil. One kind of these boundary conditions is the solid boundary condition in the proximity of the foil. This solid boundary can be considered as a wall, or as a flap or even as one or more foils in the vicinity of the main foil. Sometimes other boundary conditions such as free surface boundary condition can be considered too. In this project, first of all, we have assessed the potential flow without any boundaries over a simple, one part flapped and two part flapped airfoils by boundary element panel method and arrangement of some kinds of singular elements such as source, doublet and vortex singularities with constant and linear forms of distribution. Then, to consider the ground effect, one of the above boundary conditions, has been assessed for such foils and the results in the form of pressure coefficient and lift coefficient charts for certain foils is revealed. Consequently, the last mentioned boundary condition, i.e. the free surface boundary condition, was considered for certain hydrofoils, while the flow over a simple, one part flapped and two part flapped hydrofoil has been assessed. It is worth mentioning that one of the goals of this project was to use the Artificial Neural Networks in association with boundary integral panel method to save time and cost. Therefore, the ANN have been used with boundary integral panel method to abate time of the problem in the case of hydrofoil in the vicinity of free surface. As it is known, the Artificial Neural Network needs to be trained first. To train the ANN used in this thesis the Levenberg Marquardt algorithm is used. After that the ANN is validated by some part of data and then tested with the remaining data. The process of choosing and utilizing the neurons and other details of this part is expressed in related parts of the thesis. Then the results of panel method in combination with ANN for a simple and a two part flapped hydrofoil in the vicinity of the free surface are compared with the similar results of panel method without using the Artificial Neural Networks. Finally the use of Artificial Neural Networks in combination with other time consuming computational fluid dynamic methods, and the use of other forms of ANN is suggested for future work.Keywords: Hydrofoil, Boundary Integral Panel Method, Singular Element, Source, Doublet, Vortex, Ground Effect, Artificial Neural Network.