We consider a boundary-value problem for the nonlinear integrodifferential equation u ′ ′ ′ ′ − m ∫ 0 l u ′ 2 dx u ″ = f x u u ′ , m z ≥ α > 0 , 0 ≤ z < ∞ , simulating the static state of the Kirchhoff beam. The problem is reduced to a nonlinear integral equation, which is solved by using the Picard iterative method. The convergence of the iterative process is established and the error is estimated.