The aim of this thesis is to present two numerical approaches for solving functional Volterra-Urysohn integral equations. First, existence and uniqueness of the solution for this class of equations are studied. Then, we review Euler and trapezoidal methods for solving these equations. By these two techniques, the approximate solution of the problem under study is obtained at some considered grid points. Moreover, convergence analysis of the methods is discussed. Finally, some numerical examples are presented to confirm the validity of the numerical schemes given in the thesis.
