An iterative procedure is described for determining the lateral deflection of beams and of infinitely long, finite‐width plates under a prescribed loading. The accuracy of the method is generally expected to be better than that of the linear theory where the Bernoulli‐Euler equation is solved. The assumptions made in the procedure are that the moment curvature relationship obeys the Bernoulli‐Euler theorem, that the properties of the material do not vary throughout the entire loading history, that Hooke's law is valid, and that the spatial derivative of the deflection of any point is less than unity. An important feature of the iterative method is that it reduces the original non‐linear equation to a sequence of determinate problems involving only ordinary linear, second‐order equations for the deflection for a prescribed loading condition.