A typical mesh generation problem consists of generating triangles, quadrilaterals, tetrahedron or hexahedron elements based on the predefined piece-wised boundary of a domain. A finite element mesh is a discrete representation of a geometric domain, resulting from the subdivision of the domain into patches referred to as elements.  In recent years, a variety of methods have been introduced to generate 2D quadrilaterals for the boundary by using some predefined 'if-then' rules until the whole domain is filled with required elements. However, it is difficult to define the rules to generate a good-quality element based on all boundary information. This thesis proposes a regression model-based element extraction method for automatic finite element mesh generation that needs information from the boundary as few as possible. The method represents the 'if-then' element extraction rules and trains the relationship behind these rules. The input for the regression model includes the coordinates of some boundary points while the output defines the parameters for extracting an element. To generate good-quality elements while keeping the updated problem still solvable, the design and definition of the regression model is more complex than those in the traditional classification methods. Numerical experiments on quadrilateral mesh generation based on design of experiments demonstrate the effectiveness of the proposed method in comparison with the results obtained from existing algorithms