The aim of our work is to study two-dimensional fractured flow simulations for groundwater by using non-identical aperture of fractures via Analytic Element Method, and make a comparison between processing time of both techniques i.e. iterative and matrix method. Numerical solutions for the considered problems are totally based on series expansions, whereas the effects of every fracture are expressed as a series which obey Laplace's equation. In all examined cases, it is evident that the iterative method is not able to converge, while by introducing the matrix method, the expected results are obtained with minimum computational cost (processing time).