The analysis of static deflections of an infinite beam resting on a non-linear and discontinuous foundation is not trivial. We apply a recently proposed iterative non-linear procedure to the analysis. Mathematical models of the elastic foundation are incorporated into the governing non-linear fourth-order differential equation of the system and then the differential equation is transformed into an equivalent non-linear integral equation using Green's functions. Numerical solutions of the integral equation clearly demonstrate herein that our non-linear iterative numerical method is simple and straightforward for approximate solutions of the static deflection of an infinite beam on a non-linear elastic foundation. Iterative numerical solutions converge fast to corresponding analytic solutions. However, numerical errors are observed in a narrow neighbourhood of material discontinuities of foundations
