In this paper, an algorithm based on the regularization and Adomian decom- position methods, for handling the ill-posed two-dimensional Fredholm equations, is introduced. The application of the proposed algorithm is based on the trans- forming the first kind equation to a second kind equation by the regularization method. Then, by converting the first kind to a second kind, the Adomian method is employed to handle the resulting Fredholm integral equations of the second kind. The efficiency of the approach will be shown by applying the pro- cedure on some examples. The Mathematica program based on the procedures in this paper is designed.
