In this paper, we apply the monotone iterative method for the existence of two positive solutions of fourth-order two-point boundary value problem u′′′′ (t) = f(t, u(t)), 0 < t < 1, u(0) =u′ (0) = u′′ (1) = u′′′ (1) = 0, which models a cantilever beam equation, where one end is kept free. Here f ∈ C ([0, 1] × R+, R+). The sufficient condition is interesting, new and easy to verify. Our condition do not require any super-linearity or sub-linearity conditions on the function f at 0 or ∞. Our result uses the monotonically increasing property of f in a certain interval to prove the existence of a positive solution(s). This approach completely differs from the existing results in the literature. An example is presented at the end to illustrate the usefulness of our result. Although our theorem predicts the existence of two positive solutions, our example and the iterative scheme constructed in the example shows that the two iterative sequences of solutions converge to a single solution. © 2020, International Publications. All rights reserved.